AREA OF POLYGONS

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AREA OF POLYGONS 5.3.1 5.3.4 Area is the number of non-overlapping square units needed to cover the interior region of a twodimensional figure or the surface area of a three-dimensional figure. For example, area is the region that is covered by floor tile (two-dimensional) or paint on a box or a ball (threedimensional). For additional information about specific shapes, see the boxes below. AREA OF A RECTANGLE To find the area of a rectangle, follow the steps below. 1. Identify the. 2. Identify the. 3. Multiply the times the to find the area in square units: A = bh. A square is a rectangle in which the and are of equal length. Find the area of a square by multiplying the times itself: A = b 2. Example 4 32 square units 8 = 8 units = 4 units A = 8 4 = 32 square units 42 2013 CPM Educational Program. All rights reserved. Core Connections, Course 1

Problems Find the areas of the rectangles (figures 1-8) and squares (figures 9-12) below. 1. 2. 3. 4. 2 mi 4 mi 5 cm 7 in. 8 m 3 in. 2 m 5. 6. 7. 8. 5.5 miles 2 miles 3 units 6. 8.7 units 7.25 miles 3.5 cm 9. 10. 11. 12. 2.2 miles 8.61 feet 2.2 cm 1.5 feet 1. 8 sq. miles 2. 30 sq. cm 3. 21 sq. in. 4. 16 sq. m 5. 11 sq. miles 6. 26.1 sq. feet 7. 23.8 sq. cm 8. 15.95 sq. miles 9. 64 sq. cm 10. 4.84 sq. cm 11. 2.25 sq. feet 12. 73.96 sq. feet Parent Guide with Extra Practice 2013 CPM Educational Program. All rights reserved. 43

AREA OF A PARALLELOGRAM A parallelogram is easily changed to a rectangle by separating a triangle from one end of the parallelogram and moving it to the other end as shown in the three figures below. For additional information, see the Math Notes box in Lesson 5.3.3 of the Core Connections, Course 1 text. parallelogram move triangle rectangle Step 1 Step 2 Step 3 To find the area of a parallelogram, multiply the times the as you did with the rectangle: A = bh. Example 9 cm Problems = 9 cm = A = 9 6 = 54 square cm Find the area of each parallelogram below. 1. 2. 3. 6 feet 8 feet 10 cm 4. 5. 6. 1 7.5 in. 7. 8. 12 in. 9. 8.4 cm 11. 15.7 cm 4 m 11 m 11.2 ft 15 ft 1. 48 sq. feet 2. 80 sq. cm 3. 44 sq. m 4. 39 sq. cm 5. 90 sq. in. 6. 168 sq. ft 7. 110.74 sq. cm 8. 131.88 sq. cm 44 2013 CPM Educational Program. All rights reserved. Core Connections, Course 1

AREA OF A TRIANGLE The area of a triangle is equal to one-half the area of a parallelogram. This fact can easily be shown by cutting a parallelogram in half along a diagonal (see below). For additional information, see Math Notes box in Lesson 5.3.4 of the Core Connections, Course 1 text. parallelogram Step 1 draw a diagonal Step 2 match triangles by cutting apart or by folding Step 3 As you match the triangles by either cutting the parallelogram apart or by folding along the diagonal, the result is two congruent (same size and shape) triangles. Thus, the area of a triangle has half the area of the parallelogram that can be created from two copies of the triangle. To find the area of a triangle, follow the steps below. 1. Identify the. 2. Identify the. 3. Multiply the times the. 4. Divide the product of the times the by 2: A = bh 2 or 1 2 bh. Example 1 Example 2 = 1 = A = 16 2 8 = 128 2 = 64 cm2 1 = 7 cm = 4 cm 4 cm A = 7 2 4 = 28 2 = 14 cm2 7 cm Parent Guide with Extra Practice 2013 CPM Educational Program. All rights reserved. 45

Problems 1. 2. 3. 12 ft 14 ft 4. 5. 6. 8 in. 5 ft 17 in. 7 ft 7. 8. 5 m 1.5 m 1 9 cm 2.5 ft 21 cm 7 ft 1. 24 sq. cm 2. 84 sq. ft 3. 39 sq. cm 4. 68 sq. in. 5. 17.5 sq. ft 6. 3.75 sq. m 7. 94.5 sq. cm 8. 8.75 sq. ft 46 2013 CPM Educational Program. All rights reserved. Core Connections, Course 1

AREA OF A TRAPEZOID A trapezoid is another shape that can be transformed into a parallelogram. Change a trapezoid into a parallelogram by following the three steps below. (b) (b) (b) (b) (b) Trapezoid duplicate the trapezoid and rotate put the two trapezoids together to form a parallelogram Step 1 Step 2 Step 3 To find the area of a trapezoid, multiply the of the large parallelogram in Step 3 ( and top) times the and then take half of the total area. Remember to add the lengths of the and the top of the trapezoid before multiplying by the. Note that some texts call the top length the upper and the the lower. A = 1 2 (b + t)h or A = b + t 2 h For additional information, see the Math Notes box in Lesson 6.1.1 of the Core Connections, Course 1 text. Example 8 in. 12 in. 4 in. top = 8 in. = 12 in. = 4 in. A = 8+12 4 = 20 4 = 10 4 = 40 in.2 2 2 Parent Guide with Extra Practice 2013 CPM Educational Program. All rights reserved. 47

Problems Find the areas of the trapezoids below. 1. 2. 3. 10 in. 5 cm 5 cm 1 cm 8 in. 15 in. 4. 5. 6. 11 cm 7 in. 5 in. 15 cm 8 m 10 in. 7. 7 cm 8. 2 feet 4 feet 5 feet 11 m 8 m 8.4 cm 4 cm 10.5 cm 6.5 cm 1. 4 sq. cm 2. 100 sq. in. 3. 14 sq. feet 4. 104 sq. cm 5. 42.5 sq. in. 6. 76 sq. m 7. 35 sq. cm 8. 22.35 sq. cm. 48 2013 CPM Educational Program. All rights reserved. Core Connections, Course 1

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