Name: Period: 11.1 Area of Circles A) You will need 3 congruent circles. 1) Fold the first circle into 4 pieces. 2) Fold the 2 nd circle into 8 pieces. 3) Fold the 3 rd circle into 16 pieces Cut the pieces out. Rearrange the pieces into a different shape (not a circle) that you can calculate the area With 16 pieces, what quadrilateral can you reassemble your pieces into? B) If you were to keep dividing the circle into smaller and smaller equal pieces, write a paragraph that describes: -- describe what shape you would make -- include a diagram and label the dimensions of the quadrilateral -- what the dimensions of the circle became in your new shape -- find the area of your quadrilateral. C) Find the area of each circle. Provide the exact answer and the area rounded to the nearest tenth. 1) 2) 3) exact rounded exact rounded exact rounded https://www.youtube.com/watch?v=yokkp3pwvfc and http://pythagoreanmath.com/completeexplanation-for-area-of-a-circle-formula/ are resources for this objective
Find the area of each circle with the given information. Use your calculator's value of π. Round your answer to the nearest tenth. Show your work and include units. 1) radius = 3 km 2) radius = 10 in 3) diameter = 20 mi 4) diameter = 23.2 mi 5) circumference = 47.1 km 6) circumference = 28.3 in 7) Calculate the radius of a circle which has an area of 14 m 2. Find the circumference of each circle using the given information. Use your calculator's value of π. Round your answer to the nearest tenth. 8) area = 314.2 ft² 9) area = 387.1 ft² 10) Find the radius of a circle so that its area and circumference have the same value. (How many ways can you solve this problem? And how do you know your answer is correct?)
Name: Period: 11.2 Area of Triangles and Quadrilaterals 1. 2. 3. 4. 5. 6. Sketch and label 2 different rectangles with an area of 48 square inches. 7. 8. 9.
10. 11. 12. 13. 14. 15.
Name: Period: 11.2a Surface Area Project Introduction: You and up to two other persons will be in a group. You will use measurements and geometric formulas to predict how much paint you need to paint an object at TVHS. The two objects you may choose from: 1) 2) The paint needed for the lockers is sold in small cans, 1 can of paint can cover 70 square feet of surface. The paint needed for the wall comes in a larger container, and that container can cover 225 square feet of surface. Your task: Determine the total surface area of your objects, and predict how many cans of paint you will need based off of that calculation. Other information: You will be submitting a project poster due on The poster must have the following: 1.) A visual of the surface you are trying to paint with its dimensions labeled. 2.) Any and all calculations that demonstrate how you got your final result. 3.) An answer about how many cans of paint you will need. 4.) The poster should look like it was well put together, and should clearly explain diagrams, calculations, and answer the question. This project can t be redone. You and your group are responsible for bringing your finished work in on next block day. Please see the reverse for the rubric.
Name: Period: 11.2a Surface Area Project 0 1 2 3 4 Some Most of the elements of poster is well the display put together seem to and is project appealing. quality, while Obvious effort others do not. went into the presentation Poster Quality No poster Poster obviously lacks quality. Minimal effort Clarity of calculations and written statements (must include all calculations or default score is 0) No poster, or none of the material is decipherable or readable. The material is legible but very difficult to interpret statements. The material is consists of confusing or unclear statements that the reader may or may not be able to understand. Most of the material on the poster makes sense, but some parts may be vague or poorly connected. The entirety of the poster is of high quality. The poster makes it obvious that a week s worth of effort went into the project. The poster makes complete sense to readers, and ideas are well connected. Accuracy (must include final answer or default score is 0) No poster, No answer, or the calculations are incredibly far from the expected result The answers provided by the group are significantly far from the expected result. Attention to precision is lacking The answer is within 30% of the expected result but is a significant ways off. The answer is within 15% of the expected result, and attention to precision is obvious The answer is within 7.5% of the expected result. Attention to detail is significant Visuals No poster, or no visuals. Visuals exist but appear to be hastily made and do not help understand the solution Visuals have some useful information that help the reader understand authors solution. The visuals mostly aid in understanding. The visuals greatly help the reader understand the authors work.
Name: Period: 11.3 Apothem & Area Apothem of a Regular Polygon: A line segment from the center of a regular polygon to the midpoint of a side Draw the apothem in each regular polygon. Divide each regular polygon into isosceles triangles. Use the area of the triangles to calculate the area of the regular polygon in terms of s the side length and a the apothem Number of sides Area of regular polygon 3 4 5 6 7 *** Make a conjecture about the area of a regular polygon (A formula that will give the area of any regular n-gon) http://www.mathopenref.com/apothem.html
Find the area of each regular polygon. Round your answer to the nearest tenth if necessary. SHOW YOUR WORK. Hint for problems 7-10, you will need to use right triangle trigonometry.
Name: Period: 11.4 Applications of Area formulas 1. Tammy is estimating how much she should charge for painting 98 rooms in a new motel with one coat of base paint and one coat of finishing paint. The four walls and the ceiling of each room must be painted. Each room measures 14 ft by 18 ft by 11 ft high. a. Calculate the total area of all the surfaces to be painted with each coat. Act as if the room has no doors or windows. b. One gallon of base paint covers 600 square feet. One gallon of finishing paint covers 325 square feet. How many gallons of each will Tammy need for the job? 2. Heather s family will be installing carpet in their hallway. The carpeting they chose costs $18 per square yard, the padding $3.50 per square yard, and the installation $3 per square yard. What will it cost them to carpet the three bedrooms and the hallway shown?
3. Jack and Dianne are planning to paint the outer walls of their barn (all vertical surfaces, not the roof). The paint they have selected costs $38 per gallon and, according to the label, covers 150 square feet per gallon. will the project cost? (All measurements are in feet.) 4. It takes 65,000 solar cells, each 1.25 in. by 2.75 in., to power the Helios Prototype, shown right. How much surface area, in square feet, must be covered with the cells? The cells on Helios are 18% efficient. Suppose they were only 12% efficient, like solar cells used in homes. How much more surface area would need to be covered to deliver the same amount of power? 5. Dennis has designed this kite for a contest. He plans to cut the kite from a sheet of clear plastic and use fiberglass rods for the diagonals. He will connect all the vertices with string, and fold and glue flaps over the string. a. How much fiberglass and plastic will he need? b. Plastic is sold in rolls 36 inches wide. What length of Mylar does Dennis need for this kite?
Name: Period: 11.5 Area of Sectors Find the area of each shaded region. Show your work. The radius of each circle is r, if two circles are show, the r is the radius of the smaller circle and the R is the radius of the larger circle. 1) r = 5 2) r = 8 cm 3) r = 16cm 4) r = 2 cm 5) 6) R = 9 cm r = 4 cm
7) r = 3 cm 8) R = 13 cm 9) The shaded area is 12π r = 8 cm Find r 10) The shaded area is 11) The shaded area is 12) The shaded area is 10πcm 2 32π, find x (inner 120π and the radius The radius of the large circle diameter) is 24 cm. Find x. is 10 cm, and the radius of the small circle is 8 cm. Find x x 18 feet
Name: Period: 11.6 Area in the Coordinate Plane AREA IN THE COORDINATE WORLD 1. Find the area of triangle ABC 2. Find the area of the parallelogram 3. Find the area of the parallelogram 4. Find the area of the triangle
6. Find the area of the square 7. Find the area of the quadrilateral. 8. Find the area of the shaded region. Hints: Each side is a diameter. Find the area of the triangle as if the semi-circles were not present.
Name: Period: 11.7 Alternative Area Formulas In Ancient Egypt, when the yearly floods of the Nile River receded, the river often followed a different course, so the shape of farmers fields along the banks could change from year to year. Officials then needed to measure property areas, in order to keep records and calculate taxes. Partly to keep track of land and finances, ancient Egyptians developed some of the earliest mathematics. Historians believe that ancient Egyptian tax assessors used this formula to find the area of any quadrilateral: A = 1 2 (a + c) 1 (b + d) 2 Where a, b, c, and d are the lengths, in consecutive order, of the figure s four sides. In this activity, you will take a closer look at this ancient Egyptian formula, and another formula called Heron s formula, named after Heron of Alexandria. -- Calculating Area in Ancient Egypt Investigate the ancient Egyptian formula for quadrilaterals using Geogebra. Step 1. Construct a quadrilateral and its interior. Change the labels of the sides to a, b, c, and d, consecutively. Step 2. Click on View and make sure that the input bar is checked on the dropdown list. The bar should be displayed on the bottom of the screen. In addition, display the Algebra sidebar by going to View and selecting Area. Step 3. Using the area tool (found under Angle ), determine the area of your quadrilateral by clicking on the tool, and then clicking in the center of your polygon. Step 4. Enter the Egyptian formula for quadrilaterals into the input bar at the bottom. Type: T = 1 2 (a + c) 1 2 (b + d) The Tax Assessor s value given can be seen in the Algebra sidebar. How does the area given by this formula (T) compare to the actual area? Is the ancient Egyptian formula correct?
Step 5. Manipulate your quadrilateral and look at the changes in the relationship between the two areas. Does the ancient Egyptian formula always favor either the tax collector or the landowner? Is the ancient formula correct? Step 6. Describe the quadrilaterals for which the formula works accurately. For what kinds of quadrilaterals is it slightly inaccurate? Very inaccurate? Step 7. State the ancient Egyptian formula in words, using the word mean (as in mean, median, mode) Step 8.According to Heron s formula, if s = 1 (a + b + c), where a, b, and c are the side lengths of the 2 triangle and the area A is given by the formula A = s(s a)(s b)(s c) Use Geogebra to investigate Heron s formula. Construct a triangle and its interior. Label the sides a, b, and c, and use Area tool to fine the triangle s area. Input the formula for s = 1 (a + b + c) and then 2 enter Heron s formula H = s(s a)(s b)(s c) into the input bar (you have to use a different variable than A since it s already used). Compare the two areas. Does Heron s formula work for all triangles? To enter the square root symbol type: sqrt( ) Step 9. Devise a way for calculating the area of any quadrilateral. Use Geogebra to test your method. www.geogebra.org you can access this app from your computer or on some tablets!
Name: Period: 11. 8 Surface Area of 3D objects Prism Pyramid Cone What are the bases? What is the base? What is the base? What are the lateral faces? What are the lateral faces? What is the lateral face? To find the surface area 1) Draw and label each face of the solid as if you can cut the solid apart. Label all the dimensions 2) Calculate the area of each face. There are some faces that are identical. 3) Add the area of all the faces together. Include units. Find the surface area of each solid. Round your answer to the nearest tenth cm 2. Include units & Show work. 1) 2) 6 6 6 3) 4) The diameter of the hole is 2 cm. New faces are created. Hint: find the slant height
5) 6) What is the surface area of cardboard needed to make the duplo box? The height is 12 cm. 7) 8) What is the surface area of the Pringles can? 9 cm
Name: Period: 11.9 Area Exam Review Please use a separate sheet of paper for your work. Find the area of the shaded regions in problems 9 & 10 9. 10.
11. 12. The shaded region is 40π cm 2. Determine the radius 13. Find the area of the shaded region 14. Find the surface area of each object The hole is a square
Name(s): Period: 11.10 Cow and Shed Problems Mr. Moo is a cow tethered to the corner of Farmer Brown s barn. Farmer Brown has Mr. Moo on a 50 foot rope. Determine the total area that Mr. Moo can graze in. All units labeled on the figure are in feet. Clarissa the Cow is tethered to Farmer Jones barn. Farmer Jones has a rather interesting shape to his barn. Determine how much area Clarissa can graze in. She is on a rope that is 50 feet long.