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1 Chapter 10 This study sheet provides students and parents with the basic concepts of each chapter. Students still need to apply these skills in context. They need to know when to apply each concept, often after working through a word problem, table, chart, or graph. Some problems may be more challenging than the ones shown here, but students first need to understand these basic concepts. There are usually several ways to solve a math problem, but this guide will show you the easiest way for 6 th graders. The sections are listed in the order that I plan on teaching them, and that is subject to change. We do not use every section of the textbook. Click on the blue links to navigate through the study guide. You can also view videos at Khan Academy and Virtual Nerd. Section 10.1 Area of Parallelograms A parallelogram has 2 sets of parallel sides. Area means how many squares can cover a surface. Only the base and the height are needed. Calculate the area of this parallelogram IXL Area of Parallelograms The formula for the area of a parallelogram is Area = base height or A = bh So this parallelogram has an area of 21 ft 2, since 21 = 3 7 Here, the 5.8 for the diagonal side is not part of the formula. Khan Academy Section 10.3 Area of Triangles Area means how many squares can cover a surface. The formula for the area of a triangle is Area = base height Don t forget to include the your formula! in Calculate the area of this triangle. Buzz Math Area of Right Triangles or A = bh So this triangle has an area of 48 ft 2, since 48 = 12 8 If you forget it, your answer will be twice the value that it s supposed to be. Section 10.5 Area of Trapezoids Area means how many squares can cover a surface. The formula for the area of a trapezoid is Area = or A = (b 1 + b 2 )h (base 1 + base 2) height So this trapezoid has an area of 119 units 2, since 119 = ( ) 7 Don t worry about memorizing this formula. It will be provided for you. Just focus on identifying the 2 bases and the height. Calculate the area of this trapezoid. Khan Academy Online Math

Section 10.6 Area of Regular Polygons A regular polygon has congruent sides (all the same), and congruent angles (all the same). Regular polygons can be broken up into congruent triangles.

Again, don t forget to include the your formula! in If you forget it, your answer will be twice the value that it s supposed to be. Calculate the area of this regular pentagon.

2 Section 10.6 Area of Regular Polygons A regular polygon has congruent sides (all the same), and congruent angles (all the same). Regular polygons can be broken up into congruent triangles. Example: This hexagon can be broken up into 6 congruent triangles. Since you know the formula for a triangle, just calculate the area of 1 triangle, then multiply it by 6. Again, don t forget to include the your formula! in If you forget it, your answer will be twice the value that it s supposed to be. Calculate the area of this regular pentagon. Regular Polygons 1 Triangle = A = (8)(7) = 28 in 2 28 in 2 6 = 168 in 2 Section 10.7 Are of Composite Figures Composite figures are composed of smaller figures. So, to find the area of the composite figure, just break the figure apart into the individual shapes. Example: To find the area, break this shape into the rectangle and the triangle, since you can calculate the area of each. Area of Rectangle = 6 4 = 24 cm 2 Area of Triangle = (6)(2) = 6 cm 2 Total Area = 24 cm cm 2 =30 cm 2 You can always find the length of unknown sides. You just might have to look across the figure. Here, you know side x is 10 m, because you can look across the figure and see that its opposite side is 10 m. Calculate the shaded area of this figure. Blob Shapes Complex Figures Khan Academy Area Donuts Famobi Section 10.9 Figures on the Coordinate Plane You can plot points on a coordinate plane and connect the points to form geometric figures. Example: The points (-2, 4), (-2, -1), and (2, -1) can be connected to form a right triangle. Remember that the x-coordinate tells you to move left or right, and the y-coordinate tells you to move up or down. ( x, y ) (, ) Plot the points (-3, 3), (3, 3), (3, 1), and (-2, 1). Connect them. Identify the figure that is formed. Stock the Shelves Figures on a Plane Homer s Donuts

3 Section 10.8 Changing Dimensions If you change the dimensions of a rectangle, the area also changes. Example: If you double the length and double the width of a rectangle, the area quadruples (4 times as big). Don t just decide how the area changes based on the words you read. This is Math! Actually do the multiplication and compare the results. If you triple the length and triple the width of a 3 4 rectangle, how does the area change? Geoboards (Use 1 rubberband per shape. Double or triple the dimensions and see how the area changes.)

4 10.1 A = 35 cm 2 Click to return to the study guide.

5 square units Click to return to the study guide.

6 10.5 A = 32 square units Click to return to the study guide.

7 10.6 A = 700 cm 2 Click to return to the study guide.

8 10.7 A = 312 in 2 Click to return to the study guide. You need to calculate the area of the large, shaded rectangle, then subtract the area of the smaller, unshaded rectangle.

9 10.9 Trapezoid Click to return to the study guide.

10 10.8 It s 9 times larger than the original. Click to return to the study guide. 3 x 4 = 12 in. 2 vs 9 x 12 = 108 in. 2

GEOMETRY. slide #3. 6th Grade Math Unit 7. 6th Grade Unit 7: GEOMETRY. Name: Table of Contents. Area of Rectangles

GEOMETRY. slide #3. 6th Grade Math Unit 7. 6th Grade Unit 7: GEOMETRY. Name: Table of Contents. Area of Rectangles Name: 6th Grade Math Unit 7 GEOMETRY 2012 10 17 www.njctl.org 1 Table of Contents Area of Rectangles Area of Parallelograms Area of Triangles Area of Trapezoids Mixed Review Area of Irregular Figures Area