Chapters 1.18 and 2.18 Areas, Perimeters and Volumes
|
|
- Lionel Robert Atkinson
- 6 years ago
- Views:
Transcription
1 Chapters 1.18 and.18 Areas, Perimeters and Volumes In this chapter, we will learn about: From Text Book 1: 1. Perimeter of a flat shape: 1.A Perimeter of a square 1.B Perimeter of a rectangle 1.C Perimeter of a composite shape. Area of a flat shape:.a Area of a square.b Area of a rectangle.c Area of a composite shape 3. Different units From Text Book : 4. Area of a triangle: 4.A Area of a right triangle 4.B Area of any triangle 4.C Area of composite shapes 5. Area of a parallelogram and of a trapezium 5.A Area of a parallelogram 5.B Area of a trapezium 6. Cuboids 6.A Surface area of a cuboid 6.B Volume of a cuboid 7. The circle 7.A Definition and the elements of a circle 7.B Circumference of a circle 7.C Area of a circle 1
2 Important Note: In this chapter we will learn many new formulas. These formulas are most easily remembered by noting that they all follow the same idea of length, which will produce formulas for perimeters, the idea of surface, which will produce the formulas for areas and the idea of space occupied, which will produce the formula for volume. If we understand these 3 main ideas, memorization of these formulas is almost unnecessary. Text Book 1: 1. Perimeter of a flat shape: Definition 1: For a given flat polygon, the perimeter of the polygon if the sum of all the sides of a polygon. 1.A. Perimeter of a square: Therefore, for a square of side a as in Figure 1 : Figure 1: A square of side a The Perimeter of the square is : (1) P 4 s a 1B. Perimeter of a rectangle: For a rectangle of length l and width w as shown in Figure : Figure : A rectangle of length l and width w
3 The Perimeter of the rectangle is : () P l w l w 1.C Perimeter of a composite shape: r For a composite shape, calculate the perimeter of the shape by adding all of the sides of the shape.. Area of a flat shape: Area of a flat shape represents how many square units that flat shape occupies. Definition : The area of a polygon is the number of square units which that polygon occupies..a. Area of a square: Therefore, for a square with side a units as shown in Figure 1, (3) As a units..b Area of a rectangle: For a rectangle with length l (units) and width w (units), the area it occupies is: (4) Ar l w units. For example, a rectangle with length 3 (units) and width (units) occupies a total area of 3 6 units. Example: From Exercise set 18.1 (Text Book 1) do problems and 5..C. Area of a composite shape: We calculate the area of a composite shape either by breaking it down into a sum of rectangles, or using difference of rectangles. Worked Example (Page 156 Text Book 1): 3
4 We can do this using either sum or difference of rectangles. Example: From Exercise set 18. (Text Book 1) do problems 1, and Different units: If different units are involved, use the following transformations to bring all length to the same units, before calculating areas and / or perimeters: 1 m 100 cm (5) 1 cm 10 mm 1 m = 1000 mm Example: From Exercise Set 18.1 (Book 1) do problems 1, and 6. Text Book : 4. Area of a triangle: 4.A. Area of a right triangle: Consider a right triangle as shown in Figure 3: Figure 3: A right triangle of height h and base length b 4
5 Then its area is given by the formula: (6) A T base height Reason: See why by representing this triangle as half of a certain rectangle. 4.B. Area of any triangle: Consider a generic triangle as shown in Figure 4: Figure 4: A generic acute triangle of height h and base length b Then its area is given by the same formula: (7) A T base height Reason: See why by splitting this triangle in two right triangles (or use a different reasoning). Note that formula (7) works for an obtuse triangle as shown in Figure 5 as well. Figure 5: A generic obtuse triangle of height h and base length b Why? 5
6 Therefore, we consider formula (7) as true for the area of ANY triangle of base length b and height length h. Example: From Exercise Set 18.. A (Text Book ) do problems 1, a) and 3 and from Exercise Set 18.. B (Text Book ) do problem Area of a parallelogram and of a trapezium: 5.A. Area of a parallelogram: Figure 6: A parallelogram of height h and base length b The area of a parallelogram of height h and base length b as shown in Figure 6 above is: (8) AP b h To see why, see that the area of this parallelogram is the area of a rectangle with length b and width h. 5.B. Area of a trapezium: 6
7 Figure 7: A trapezium with length of parallel sides a and b and with height h The area of a trapezium as shown in Figure 7 above is: (8) A Trapezium a b h To see why, split the trapezium into a rectangle and two right triangles. Note: Memorize the area formulas: (3), (4), (6), (7) and (8) as we will use these often. Example: From Exercise Set 18.3 A in Text Book do problems 1 and 3 and from Exercise Set B do problem. 6.Cuboids: A cuboid is a 3 dimensional box as shown in Figure 8. Figure 8: A cuboid of length l, width w and height h. 6.A. Surface area of a cuboid Its surface area is the sum of the areas of its faces (that is the total area covered by its faces, if the cuboid were to be expanded over a D flat surface). We can see that the surface area of a general cuboid of length l, width w and height h is: (9) S l w l h w h l w l h w h C Example: Consider the cuboid shown below: units 7
8 Figure 9: A specific cuboid Calculate its surface area. 6.B Volume of a cuboid: The volume of a cuboid is the number of cube units (that is the number of cubes of a side of length 1 unit) which it contains. The volume of a cuboid of length l, width w and height h is given by the formula: (10) V l w h 3 units Example: From Exercise Set 18.4 do problems 1 and The Circle 7.A. Definition and elements of a circle: As we have seen in Chapter 10, we have: Definition: Given a fixed point in plane O, and a positive number (the radius of the circle R), the circle with center O and radius R is the set of points in plane P which are at the fixed distance r from O, so for which: OP R. A generic circle is shown in Figure 10 below: 8
9 Figure 10: A circle of center O and radius R. We already see certain elements of the circle: the center O, the radius R (which is also the segment OP), the diameter D (which is the segment through the center of the circle which has as endpoints two points on the circle), and the circumference C (the circumference can be thought of as the perimeter of the circle). Other elements of the circle are shown in Figure 11 below. 9
10 Figure 11: Main elements of a circle. Describe in your words: the chord of a circle, the segment of a circle, the arc of a circle, the sector of a circle, and the tangent to a circle. Example: Do Exercise 18.5.A from Book. 7.B. The circumference of a circle: Activity 1: Let us measure the circumference of a circle. We need: 7. One cylinder (cup) or a bicycle wheel; 8. One piece of string; 9. A ruler; 10. Paper and pencil. Steps: Step 1: Measure the diameter of the circle; Step : Wrap the string tightly around the edge of the cylinder and measure the circumference of the circle. Step 3: Record your results; Step 4: Divide the circumference to the diameter. What number did you obtain? This should produce the following formula for the circumference of a circle: (11) C D R Example: From Exercise Set B (Book ) do exercises 1 b, d, and c. 7.C. The area of a circle: In order to find the area of a circle, we split it in many sectors. More sectors we consider, better the approximation of our final formula will be. Consider Figure 1 below: 10
11 Figure 1: Deriving the formula for the area of a circle. Note that the number of sectors is the same in the top and bottom figures. This suggests the following formula for the area of a circle of radius R: (1) Ac R Example: From Exercise Set 18.5 C do exercises a, e and f. Homework: What is left from Exercises above and from Text Book 1: Exercise Set 18.1: problems 3 and 4, and Exercise Set 18.: problems 3 and 4. From Text Book : Exercise Set 18. : problem, Exercise Set 18.3.A : problem, Exercise Set B: problems 1 and 3, Exercise Set 18.4: problems and 6. 11
Properties of a Circle Diagram Source:
Properties of a Circle Diagram Source: http://www.ricksmath.com/circles.html Definitions: Circumference (c): The perimeter of a circle is called its circumference Diameter (d): Any straight line drawn
More informationPages do a,c,e only (for questions that have parts)
use their knowledge of rectangles, parallelograms and triangles to deduce formulae for the area of a parallelogram, and a triangle, from the formula for the area of a rectangle solve problems involving
More informationSHAPE, SPACE and MEASUREMENT
SHAPE, SPACE and MEASUREMENT Types of Angles Acute angles are angles of less than ninety degrees. For example: The angles below are acute angles. Obtuse angles are angles greater than 90 o and less than
More informationGeometry 10 and 11 Notes
Geometry 10 and 11 Notes Area and Volume Name Per Date 10.1 Area is the amount of space inside of a two dimensional object. When working with irregular shapes, we can find its area by breaking it up into
More informationGeometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.
Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know
More informationLines Plane A flat surface that has no thickness and extends forever.
Lines Plane A flat surface that has no thickness and extends forever. Point an exact location Line a straight path that has no thickness and extends forever in opposite directions Ray Part of a line that
More informationReview of 7 th Grade Geometry
Review of 7 th Grade Geometry In the 7 th Grade Geometry we have covered: 1. Definition of geometry. Definition of a polygon. Definition of a regular polygon. Definition of a quadrilateral. Types of quadrilaterals
More informationWrite down a formula for the surface area of a Prism and a Cylinder
Write down a formula for the surface area of a Prism and a Cylinder Quiz Thursday Naming Figures Cross Sections Nets Lateral Area, Surface Area Prisms and cylinders have 2 congruent parallel bases. A lateral
More informationacute angle An angle with a measure less than that of a right angle. Houghton Mifflin Co. 2 Grade 5 Unit 6
acute angle An angle with a measure less than that of a right angle. Houghton Mifflin Co. 2 Grade 5 Unit 6 angle An angle is formed by two rays with a common end point. Houghton Mifflin Co. 3 Grade 5 Unit
More informationSPRINGBOARD UNIT 5 GEOMETRY
SPRINGBOARD UNIT 5 GEOMETRY 5.1 Area and Perimeter Perimeter the distance around an object. To find perimeter, add all sides. Area the amount of space inside a 2 dimensional object. Measurements for area
More informationDraw 3 rectangles with area 30cm 2.
Area area 1 Area of rectangles and compound shapes Find the area of each shape 5cm 2cm 7m 0.5m 5m 6m Draw 3 rectangles with area 30cm 2. 2 Area of Parallelograms gsp Area of a parallelogram = Page 74 A2
More informationSurface Area and Volume
Surface Area and Volume Day 1 - Surface Area of Prisms Surface Area = The total area of the surface of a three-dimensional object (Or think of it as the amount of paper you ll need to wrap the shape.)
More informationGeometry Surface Area and Volume of Pyramids and Cones.
Geometry 11.6 Surface Area and Volume of Pyramids and Cones mbhaub@mpsaz.org 11.6 Essential Question How do you find the surface area and volume of a pyramid or a cone? Geometry 1.3 Surface Area of Pyramids
More informationSolve 3-D problems using Pythagoras theorem and trigonometric ratios (A*) Solve more complex 2-D problems using Pythagoras theorem & trigonometry (A)
Moving from A to A* Solve 3-D problems using Pythagoras theorem and trigonometric ratios (A*) A* Use the sine & cosine rules to solve more complex problems involving non right-angled triangles (A*) Find
More informationPA Core Standards For Mathematics Curriculum Framework Geometry
Patterns exhibit relationships How can patterns be used to describe Congruence G.1.3.1.1 and Similarity G.1.3.1.2 described, and generalized. situations? G.1.3.2.1 Use properties of congruence, correspondence,
More informationPLC Papers. Created For:
PLC Papers Created For: 3D shapes 2 Grade 4 Objective: Identify the properties of 3-D shapes Question 1. The diagram shows four 3-D solid shapes. (a) What is the name of shape B.. (1) (b) Write down the
More informationGeometry Workbook WALCH PUBLISHING
Geometry Workbook WALCH PUBLISHING Table of Contents To the Student..............................vii Unit 1: Lines and Triangles Activity 1 Dimensions............................. 1 Activity 2 Parallel
More informationUnit 7: 3D Figures 10.1 & D formulas & Area of Regular Polygon
Unit 7: 3D Figures 10.1 & 10.2 2D formulas & Area of Regular Polygon NAME Name the polygon with the given number of sides: 3-sided: 4-sided: 5-sided: 6-sided: 7-sided: 8-sided: 9-sided: 10-sided: Find
More informationAnswer Section. Honors Geometry Final Study Guide 2013 Solutions and Section References 1. ANS: 900
Honors Geometry Final Study Guide 2013 Solutions and Section References Answer Section 1. ANS: 900 2. ANS: 6300 3. ANS: B 4. ANS: x = 111, y = 64 5. ANS: 45 6. ANS: 110 7. ANS: REF: 6-2 Properties of Parallelograms
More informationSect Volume. 3 ft. 2 ft. 5 ft
199 Sect 8.5 - Volume Objective a & b: Understanding Volume of Various Solids The Volume is the amount of space a three dimensional object occupies. Volume is measured in cubic units such as in or cm.
More informationPrime Time (Factors and Multiples)
CONFIDENCE LEVEL: Prime Time Knowledge Map for 6 th Grade Math Prime Time (Factors and Multiples). A factor is a whole numbers that is multiplied by another whole number to get a product. (Ex: x 5 = ;
More informationS8.6 Volume. Section 1. Surface area of cuboids: Q1. Work out the surface area of each cuboid shown below:
Things to Learn (Key words, Notation & Formulae) Complete from your notes Radius- Diameter- Surface Area- Volume- Capacity- Prism- Cross-section- Surface area of a prism- Surface area of a cylinder- Volume
More informationMeasurement 1 PYTHAGOREAN THEOREM. The area of the square on the hypotenuse of a right triangle is equal to the sum of the areas of
Measurement 1 PYTHAGOREAN THEOREM Remember the Pythagorean Theorem: The area of the square on the hypotenuse of a right triangle is equal to the sum of the areas of the squares on the other two sides.
More informationMoore Catholic High School Math Department
Moore Catholic High School Math Department Geometry Vocabulary The following is a list of terms and properties which are necessary for success in a Geometry class. You will be tested on these terms during
More informationThe figures below are all prisms. The bases of these prisms are shaded, and the height (altitude) of each prism marked by a dashed line:
Prisms Most of the solids you ll see on the Math IIC test are prisms or variations on prisms. A prism is defined as a geometric solid with two congruent bases that lie in parallel planes. You can create
More information3. Area and perimeter.notebook November 13, All rectangles with area 12cm 2 have the same perimeter. True or false?
All rectangles with area 12cm 2 have the same perimeter. True or false? Find the perimeter of the shape: Draw another shape with area a smaller perimeter. but with x y Write an expression for the perimeter
More informationchange divided by original times 100 divide by the bottom, times by the top Divide both the top and bottom of a fraction by the same number
Averages and Range How do you work out the mean? How do you get the mode? How do you work out the median? How do you work out the range? How do you work out the mean for a frequency table? Add up all the
More informationThe radius for a regular polygon is the same as the radius of the circumscribed circle.
Perimeter and Area The perimeter and area of geometric shapes are basic properties that we need to know. The more complex a shape is, the more complex the process can be in finding its perimeter and area.
More informationDO NOW Geometry Regents Lomac Date. due. 3D: Area, Dissection, and Cavalieri
DO NOW Geometry Regents Lomac 2014-2015 Date. due. 3D: Area, Dissection, and Cavalieri (DN) ON BACK OF PACKET Name Per LO: I can define area, find area, and explain dissection and Cavalieri s Principle
More informationFind the area and perimeter of these shapes: Draw another shape with area a smaller perimeter. a larger perimeter.
Find the area and perimeter of these shapes: Draw another shape with area a smaller perimeter. Draw another shape with area a larger perimeter. but with but with Page 1 Perimeter 10cm 2cm 5cm An equilateral
More informationUnit 10 Study Guide: Plane Figures
Unit 10 Study Guide: Plane Figures *Be sure to watch all videos within each lesson* You can find geometric shapes in art. Whether determining the amount of leading or the amount of glass needed for a piece
More informationEVERYTHING YOU NEED TO KNOW TO GET A GRADE C GEOMETRY & MEASURES (FOUNDATION)
EVERYTHING YOU NEED TO KNOW TO GET A GRADE C GEOMETRY & MEASURES (FOUNDATION) Rhombus Trapezium Rectangle Rhombus Rhombus Parallelogram Rhombus Trapezium or Rightangle Trapezium 110 250 Base angles in
More informationGeometry: Semester 2 Practice Final Unofficial Worked Out Solutions by Earl Whitney
Geometry: Semester 2 Practice Final Unofficial Worked Out Solutions by Earl Whitney 1. Wrapping a string around a trash can measures the circumference of the trash can. Assuming the trash can is circular,
More informationTeeJay Publishers Homework for Level D book Ch 10-2 Dimensions
Chapter 10 2 Dimensions Exercise 1 1. Name these shapes :- a b c d e f g 2. Identify all the 2 Dimensional mathematical shapes in these figures : (d) (e) (f) (g) (h) 3. Write down the special name for
More informationPre-Algebra, Unit 10: Measurement, Area, and Volume Notes
Pre-Algebra, Unit 0: Measurement, Area, and Volume Notes Triangles, Quadrilaterals, and Polygons Objective: (4.6) The student will classify polygons. Take this opportunity to review vocabulary and previous
More informationWorksheets for GCSE Mathematics. Perimeter & Area. Mr Black's Maths Resources for Teachers GCSE 1-9. Shape
Worksheets for GCSE Mathematics Perimeter & Area Mr Black's Maths Resources for Teachers GCSE 1-9 Shape Perimeter & Area Worksheets Contents Differentiated Independent Learning Worksheets Perimeter of
More informationBMGM-2 BMGM-3 BMGM-1 BMGM-7 BMGM-6 BMGM-5 BMGM-8 BMGM-9 BMGM-10 BMGM-11 DXGM-7 DXGM-23 BMGM-12 BMGM-13 BMGM-14 BMGM-15 BMGM-16 DXGM-9
Objective Code Advance BMGM-2 BMGM-3 BMGM-1 BMGM-7 BMGM-6 BMGM-5 BMGM-8 BMGM-9 BMGM-10 BMGM-11 DXGM-7 DXGM-8 BMGM-12 BMGM-13 BMGM-14 BMGM-15 BMGM-16 DXGM-9 DXGM-10 DXGM-11 DXGM-15 DXGM-17 DXGM-16 DXGM-18
More information1. AREAS. Geometry 199. A. Rectangle = base altitude = bh. B. Parallelogram = base altitude = bh. C. Rhombus = 1 product of the diagonals = 1 dd
Geometry 199 1. AREAS A. Rectangle = base altitude = bh Area = 40 B. Parallelogram = base altitude = bh Area = 40 Notice that the altitude is different from the side. It is always shorter than the second
More informationGeometry B. The University of Texas at Austin Continuing & Innovative Education K 16 Education Center 1
Geometry B Credit By Exam This Credit By Exam can help you prepare for the exam by giving you an idea of what you need to study, review, and learn. To succeed, you should be thoroughly familiar with the
More informationA triangle that has three acute angles Example:
1. acute angle : An angle that measures less than a right angle (90 ). 2. acute triangle : A triangle that has three acute angles 3. angle : A figure formed by two rays that meet at a common endpoint 4.
More informationMensuration: Basic Concepts and Important Formulas
Equilateral Triangle: All the three sides are equal and each angle is equal to. Height (Altitude) = 3(side) Isosceles Triangle: Two sides and two angles are equal and altitude drawn on nonequal side bisects
More informationFoundation Chapter 19 Simple perimeter, area and volume
Foundation Chapter 19 Simple perimeter, area and volume Background This chapter shows how to find the perimeter and area of simple composite 2 D shapes, and the volume of a cuboid. Surface areas of simple
More informationExtra Practice 1. Name Date. Lesson 1: Exploring Triangles
Master 6.36 Extra Practice 1 Lesson 1: Exploring Triangles 1. Draw 3 different triangles. Measure and label the side lengths. Name each triangle as equilateral, isosceles, or scalene. 2. Name each triangle
More informationMrs. Daniel s Geometry Vocab List
Mrs. Daniel s Geometry Vocab List Geometry Definition: a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Refectional Symmetry Definition:
More informationGeometry Vocabulary Math Fundamentals Reference Sheet Page 1
Math Fundamentals Reference Sheet Page 1 Acute Angle An angle whose measure is between 0 and 90 Acute Triangle A that has all acute Adjacent Alternate Interior Angle Two coplanar with a common vertex and
More informationChapter 7. Description or Example. Found on Page. Vocabulary Term. Definition. base. center. circumference. chord. complex figure. cone.
C H A P T E R 7 This is an alphabetical list of new vocabulary terms you will learn in Chapter 7. As you complete the study notes for the chapter, you will see Build Your Vocabulary reminders to complete
More informationPre-Algebra Notes Unit 10: Geometric Figures & Their Properties; Volume
Pre-Algebra Notes Unit 0: Geometric Figures & Their Properties; Volume Triangles, Quadrilaterals, and Polygons Syllabus Objectives: (4.6) The student will validate conclusions about geometric figures and
More informationVocabulary. Triangular pyramid Square pyramid Oblique square pyramid Pentagonal pyramid Hexagonal Pyramid
CP1 Math 2 Unit 8: S.A., Volume, Trigonometry: Day 7 Name Surface Area Objectives: Define important vocabulary for 3-dimensional figures Find the surface area for various prisms Generalize a formula for
More informationSupporting planning for shape, space and measures in Key Stage 4: objectives and key indicators
1 of 7 Supporting planning for shape, space and measures in Key Stage 4: objectives and key indicators This document provides objectives to support planning for shape, space and measures in Key Stage 4.
More informationUnit 4 End-of-Unit Assessment Study Guide
Circles Unit 4 End-of-Unit Assessment Study Guide Definitions Radius (r) = distance from the center of a circle to the circle s edge Diameter (d) = distance across a circle, from edge to edge, through
More informationGeometry End of Course Review
1 Area of a rectangle is equal to base x height. For a triangle Area = ½ (bh) or one half base x height. The height must be the perpendicular distance from the base to the tallest part. The area of a circle
More information1.4 Perimeter, Area and Surface Area of Similar Figures
Foundations of Math Section.4 Perimeter, rea and Surface rea of Similar Figures 35.4 Perimeter, rea and Surface rea of Similar Figures The squares shown below are similar. The corresponding sides are in
More informationMATH DICTIONARY. Number Sense. Number Families. Operations. Counting (Natural) Numbers The numbers we say when we count. Example: {0, 1, 2, 3, 4 }
Number Sense Number Families MATH DICTIONARY Counting (Natural) Numbers The numbers we say when we count Example: {1, 2, 3, 4 } Whole Numbers The counting numbers plus zero Example: {0, 1, 2, 3, 4 } Positive
More informationMrs. Daniel s Geometry Vocab List
Mrs. Daniel s Geometry Vocab List Geometry Definition: a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Reflectional Symmetry
More informationArea of Polygons And Circles
Name: Date: Geometry 2011-2012 Area of Polygons And Circles Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the area and perimeter of Parallelograms and Triangles Pgs: 1-5 HW: Pgs: 6-7 DAY
More informationOhio s Learning Standards-Extended. Mathematics. Congruence Standards Complexity a Complexity b Complexity c
Ohio s Learning Standards-Extended Mathematics Congruence Standards Complexity a Complexity b Complexity c Most Complex Least Complex Experiment with transformations in the plane G.CO.1 Know precise definitions
More informationHigh School Geometry. Correlation of the ALEKS course High School Geometry to the ACT College Readiness Standards for Mathematics
High School Geometry Correlation of the ALEKS course High School Geometry to the ACT College Readiness Standards for Mathematics Standard 5 : Graphical Representations = ALEKS course topic that addresses
More informationIndex COPYRIGHTED MATERIAL. Symbols & Numerics
Symbols & Numerics. (dot) character, point representation, 37 symbol, perpendicular lines, 54 // (double forward slash) symbol, parallel lines, 54, 60 : (colon) character, ratio of quantity representation
More information11.4 Volume of Prisms and Cylinders
11.4 Volume of Prisms and Cylinders Learning Objectives Find the volume of a prism. Find the volume of a cylinder. Review Queue 1. Define volume in your own words. 2. What is the surface area of a cube
More informationMath 1 Plane Geometry Part 1
Math 1 Plane Geometry Part 1 1 Intersecting lines: When two lines intersect, adjacent angles are supplementary (they make a line and add up to 180 degrees, and vertical angles (angles across from each
More informationVocabulary. Term Page Definition Clarifying Example. apothem. center of a circle. center of a regular polygon. central angle of a regular polygon
CHAPTER 9 Vocabulary The table contains important vocabulary terms from Chapter 9. As you work through the chapter, fill in the page number, definition, and a clarifying example. apothem Term Page Definition
More informationGrade VIII. Mathematics Geometry Notes. #GrowWithGreen
Grade VIII Mathematics Geometry Notes #GrowWithGreen Polygons can be classified according to their number of sides (or vertices). The sum of all the interior angles of an n -sided polygon is given by,
More informationPerimeter, Area, Surface Area, & Volume
Additional Options: Hide Multiple Choice Answers (Written Response) Open in Microsoft Word (add page breaks and/or edit questions) Generation Date: 11/25/2009 Generated By: Margaret Buell Copyright 2009
More informationLength and Area. Charles Delman. April 20, 2010
Length and Area Charles Delman April 20, 2010 What is the length? Unit Solution Unit 5 (linear) units What is the length? Unit Solution Unit 5 2 = 2 1 2 (linear) units What is the perimeter of the shaded
More informationCORRELATION TO GEORGIA QUALITY CORE CURRICULUM FOR GEOMETRY (GRADES 9-12)
CORRELATION TO GEORGIA (GRADES 9-12) SUBJECT AREA: Mathematics COURSE: 27. 06300 TEXTBOOK TITLE: PUBLISHER: Geometry: Tools for a Changing World 2001 Prentice Hall 1 Solves problems and practical applications
More informationLesson 10T ~ Three-Dimensional Figures
Lesson 10T ~ Three-Dimensional Figures Name Period Date Use the table of names at the right to name each solid. 1. 2. Names of Solids 3. 4. 4 cm 4 cm Cone Cylinder Hexagonal prism Pentagonal pyramid Rectangular
More informationUnit 9 Study Guide. Multiple Choice (2 points) Identify the choice that best completes the statement or answers the question.
Unit 9 Study Guide Multiple hoice (2 points) Identify the choice that best completes the statement or answers the question. Find the perimeter of each rectangle. 1. 38 m 18 m a. 684 m c. 56 m b. 94 m d.
More informationSTRAND E: Measurement. UNIT 13 Areas Student Text Contents. Section Squares, Rectangles and Triangles Area and Circumference of Circles
UNIT 13 Areas Student Text Contents STRAND E: Measurement Unit 13 Areas Student Text Contents Section 13.1 Squares, Rectangles and Triangles 13. Area and Circumference of Circles 13.3 Sector Areas and
More informationVocabulary for Geometry. Line (linea) a straight collection of points extending in opposite directions without end.
Vocabulary for Geometry Line (linea) a straight collection of points extending in opposite directions without end. A line AB or line BA B Symbol for a line is AB Jan 27 2:56 PM Line Segment (linea segmento)
More informationGrades 7 & 8, Math Circles 20/21/22 February, D Geometry
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing 2D Geometry Review Grades 7 & 8, Math Circles 20/21/22 February, 2018 3D Geometry Two-dimensional shapes
More informationT103 Final Review Sheet. Central Angles. Inductive Proof. Transversal. Rectangle
T103 Final Review Sheet Know the following definitions and their notations: Point Hexa- Space Hepta- Line Octa- Plane Nona- Collinear Deca- Coplanar Dodeca- Intersect Icosa- Point of Intersection Interior
More informationSHAPE AND STRUCTURE. Shape and Structure. An explanation of Mathematical terminology
Shape and Structure An explanation of Mathematical terminology 2005 1 POINT A dot Dots join to make lines LINE A line is 1 dimensional (length) A line is a series of points touching each other and extending
More informationLesson 9. Three-Dimensional Geometry
Lesson 9 Three-Dimensional Geometry 1 Planes A plane is a flat surface (think tabletop) that extends forever in all directions. It is a two-dimensional figure. Three non-collinear points determine a plane.
More informationDate Lesson Text TOPIC Homework. SA of Prisms & Pyramids Pg. 441 # 1, 3, 5a, 7b, 11bc, 16. Surface Area of Cylinders WS 6.6
UNIT 6 MEASUREMENT Date Lesson Text TOPIC Homework May 6.1 8.1 May 4 6. 8. The Pythagorean Theorem Pg. 4 # 1ac, ac, ab, 4ac, 5, 7, 8, 10 Perimeter and Area (NO CIRCLES) Pg. 4 # 1acde, abdf,, 4, 11, 14,
More information6. If QRSTU is a regular pentagon, what is the measure of T? 1. If STUV is a parallelogram, what are the coordinates of point U?
1. If UV is a parallelogram, what are the coordinates of point U?. If RU is a regular pentagon, what is the measure of? (0, y) U(?,?) (, 0) V( + z, 0) 7. hree siblings are to share an inheritance of $1,0
More information(based on Assessment Criteria)
NO. OF GRADE 10 ASSESSMENT SESSIONS (MATHEMATICS) INTERDISCIPLINARY 25 TOPIC- GEOMETRY AOI- Human Ingenuity SIGNIFICANT CONCEPTS- Geometry allows us to work out the relationships Between shapes, forms
More informationSTANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS GEOMETRY. 3 rd Nine Weeks,
STANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS GEOMETRY 3 rd Nine Weeks, 2016-2017 1 OVERVIEW Geometry Content Review Notes are designed by the High School Mathematics Steering Committee as a resource
More informationA plane that is to the base of the figure will create a cross section that is the same shape as the base.
Objective: 9.1 3 Notes: Surface Area of Solids Name Cross Sections: A cuts through a solid figure to create a cross section. Depending on the way in which the plane cuts through the figure will determine
More information12 m. 30 m. The Volume of a sphere is 36 cubic units. Find the length of the radius.
NAME DATE PER. REVIEW #18: SPHERES, COMPOSITE FIGURES, & CHANGING DIMENSIONS PART 1: SURFACE AREA & VOLUME OF SPHERES Find the measure(s) indicated. Answers to even numbered problems should be rounded
More informationAngles, Polygons, Circles
Page 1 of 5 Part One Last week we learned about the angle properties of circles and used them to solve a simple puzzle. This week brings a new puzzle that will make us use our algebra a bit more. But first,
More informationMath 3315: Geometry Vocabulary Review Human Dictionary: WORD BANK
Math 3315: Geometry Vocabulary Review Human Dictionary: WORD BANK [acute angle] [acute triangle] [adjacent interior angle] [alternate exterior angles] [alternate interior angles] [altitude] [angle] [angle_addition_postulate]
More informationMeasurement and Geometry: Area and Volume of Geometric Figures and Objects *
OpenStax-CNX module: m35023 1 Measurement and Geometry: and Volume of Geometric Figures and Objects * Wade Ellis Denny Burzynski This work is produced by OpenStax-CNX and licensed under the Creative Commons
More informationMathematics Department Inverclyde Academy
Common Factors I can gather like terms together correctly. I can substitute letters for values and evaluate expressions. I can multiply a bracket by a number. I can use common factor to factorise a sum
More informationRead, write, order and compare numbers up to and determine the value of each digit. Round any whole number to a required degree of accuracy
Autumn Term Area Year 6 Year 5 Number and place value Addition Multiplication and division up to 10 000 000 and determine the value of each digit Round any whole number to a required degree of accuracy
More informationTo find the surface area of a pyramid and a cone
11-3 Surface Areas of Pyramids and Cones Common Core State Standards G-MG.A.1 Use geometric shapes, their measures, and their properties to describe objects. MP 1, MP 3, MP 4, MP 6, MP 7 Objective To find
More informationChapter 11. Area of Polygons and Circles
Chapter 11 Area of Polygons and Circles 11.1 & 11.2 Area of Parallelograms, Triangles, Trapezoids, Rhombi, and Kites Use your formula chart to find the formula for the Areas of the following Polygons
More informationNumber. Number. Number. Number
Order of operations: Brackets Give the order in which operations should be carried out. Indices Divide Multiply Add 1 Subtract 1 What are the first 10 square numbers? The first 10 square numbers are: 1,
More informationPlot four points A, B, C and D on the grid to make a rectangle ABCD of length 6 cm and width 4 cm. (2)
Q1. (a) Here is a centimetre grid. Plot four points A, B, C and D on the grid to make a rectangle ABCD of length 6 cm and width 4 cm. (2) (b) Tick whether each statement is always true, sometimes true
More informationAreas of Rectangles and Parallelograms
CONDENSED LESSON 8.1 Areas of Rectangles and Parallelograms In this lesson, you Review the formula for the area of a rectangle Use the area formula for rectangles to find areas of other shapes Discover
More informationSOLID SHAPES M.K. HOME TUITION. Mathematics Revision Guides. Level: GCSE Foundation Tier
Mathematics Revision Guides Solid Shapes Page 1 of 15 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Foundation Tier SOLID SHAPES Version: 1. Date: 10-11-2015 Mathematics Revision Guides Solid
More informationC in. 2. D in Find the volume of a 7-inch tall drinking glass with a 4-inch diameter. C lateral faces. A in. 3 B in.
Standardized Test A For use after Chapter Multiple Choice. Which figure is a polyhedron? A B 7. Find the surface area of the regular pyramid. A 300 ft 2 B 340 ft 2 C 400 ft 2 C D D 700 ft 2 2. A polyhedron
More informationAnswer Key. 1.1 The Three Dimensions. Chapter 1 Basics of Geometry. CK-12 Geometry Honors Concepts 1. Answers
1.1 The Three Dimensions 1. Possible answer: You need only one number to describe the location of a point on a line. You need two numbers to describe the location of a point on a plane. 2. vary. Possible
More information2. a. approximately cm 3 or 9p cm b. 20 layers c. approximately cm 3 or 180p cm Answers will vary.
Answers Investigation ACE Assignment Choices Problem. Core Other Connections Problem. Core,, Other Applications 7, ; Connections 7 0; unassigned choices from previous problems Problem. Core 7 Other Connections,
More informationFebruary 07, Dimensional Geometry Notebook.notebook. Glossary & Standards. Prisms and Cylinders. Return to Table of Contents
Prisms and Cylinders Glossary & Standards Return to Table of Contents 1 Polyhedrons 3-Dimensional Solids A 3-D figure whose faces are all polygons Sort the figures into the appropriate side. 2. Sides are
More informationGeometry Term 2 Final Exam Review
Geometry Term Final Eam Review 1. If X(5,4) is reflected in the line y =, then find X.. (5,). (5,0). (-1,) D. (-1,4) Name 6. Find the tangent of angle X. Round your answer to four decimal places. X. 0.5
More informationContents. Lines, angles and polygons: Parallel lines and angles. Triangles. Quadrilaterals. Angles in polygons. Congruence.
Colegio Herma. Maths Bilingual Departament Isabel Martos Martínez. 2015 Contents Lines, angles and polygons: Parallel lines and angles Triangles Quadrilaterals Angles in polygons Congruence Similarity
More informationKansas City Area Teachers of Mathematics 2010 KCATM Math Competition
Kansas ity rea Teachers of Mathematics 2010 KTM Math ompetition GEOMETRY N MESUREMENT TEST GRE 5 INSTRUTIONS o not open this booklet until instructed to do so. Time limit: 15 minutes You may use calculators
More information2x + 3x = 180 5x = (5x) = 1 5 (180) x = 36. Angle 1: 2(36) = 72 Angle 2: 3(36) = 108
GRADE 7 MODULE 6 TOPIC A LESSONS 1 4 KEY CONCEPT OVERVIEW In this topic, students return to using equations to find unknown angle measures. Students write equations to model various angle relationships
More informationEuclid s Muse Directions
Euclid s Muse Directions First: Draw and label three columns on your chart paper as shown below. Name Picture Definition Tape your cards to the chart paper (3 per page) in the appropriate columns. Name
More informationGanado Unified School District 7 th Grade Mathematics
Ganado Unified School District 7 th Grade Mathematics PACING Guide SY 2014-2015 Quarter 3 Week 1 Graphs Text Reference Concept : Use random sampling to draw inferences about population. 7.SP.A.1. Understand
More information