Perimeter. Name. 22 Topic 17. Reteaching Find the perimeter of the figure below.

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1 Perimeter Reteaching 1-1 Find the perimeter of the figure below. 15 m x 4 ft 4 ft 2 ft y 2 ft 5 ft 6 m 20 ft Reteaching 1-1 By using a formula: There are two equal lengths and equal widths, so you can use the formula P 2l 2w. P 2(6) 2(15) The perimeter is 42 m. Sometimes you are not given the lengths of all the sides of a polygon. Side x is the same size as the side parallel to it. So, side x 5 ft. You can figure out the length of side y by looking at the side parallel to it. That side is 20 ft. 4 ft 4 ft y ft 20 ft 8 ft y ft 20 ft 8 ft 12 ft 20 ft So, y 12 ft. Now you can add up all the sides to find the perimeter P 54 ft Find the perimeter of each figure. 1. rectangle, length 5.1 ft, width.4 ft 2. regular octagon, sides 4.6 cm long Find the length of each unknown side. Then find the perimeter m 4. m x 15 m 10 m 4 m 3 in. 2 in. 12 in. 2 in. 2 in. y 3 in. 2 in. 22 Topic 1

2 Perimeter Find the perimeter of each figure. Practice rectangle 2. regular pentagon 3. regular octagon length 6 in., width 14 in. sides 3.3 cm long sides 8 3_ in. long 4 Estimate the perimeter of each figure. Then find the perimeter m cm Practice m cm cm 18.9 cm Find the length of each unknown side. Then find the perimeter. 6. y. 12 ft 18 mm 39 mm 15 mm 4 mm z j 9 ft 6 ft k 14 ft 8. One side of a regular hexagon is 18 cm. Which is the perimeter? A 108 cm B 96 cm C 2 cm D 36 cm 9. Writing to Explain A square and a rectangle each have a perimeter of 100 ft. Explain how this is possible. Topic 1 23

3 Area of Rectangles and Irregular Figures Reteaching 1-2 Find the area of a rectangle that is 8 inches long and 3 inches wide. Use Counting Draw the rectangle on graph paper. Let each square represent 1 square inch. A path around a garden measures 8 ft by ft. The garden measures 4 ft by 3 ft. What is the area of the path? Use Counting Draw the figure on graph paper. Let each square represent 1 square foot. Reteaching inches 3 inches Count the squares inside the rectangle. There are 24 squares, so the area is 24 sq in. Use a Formula Use the formula for area.to find area, multiply length times width. A 5 l 3 w l 5 length, w 5 width A l 5 8, w 5 3 A 5 24 The area of the rectangle is 24 sq in. 4 ft 3 ft feet 8 feet Count the squares in the path only. There are 44 squares, so the area is 44 sq ft. Use a Formula Find the area of the path and the garden together. Then subtract the area of the garden. Path: Display: A 5 l 3 w A 5 l 3 w A A A 5 56 sq ft A 5 12 sq ft , so the area is 44 sq ft. Find the area of each figure mm m 21 m 20 m 14 mm 25 yd 19 m 12 yd 4. Suppose a rectangular path around a rectangular garden measures 4 meters by meters. The garden measures 3 meters by 6 meters. What is the area of the path? 28 Topic 1

4 Area of Rectangles and Irregular Figures Find the area of each figure Practice mi 14 mi 15 in m in. cm Practice m 30 cm 20 cm 5 m 50 m 38 cm 6 cm For 5 and 6, draw and label the figures described using graph paper. Then calculate the area of each figure. 5. A rectangle that is 13 units by 9 units 6. Carlos is laminating a kitchen counter that has dimensions of 12 feet by 3 feet. The counter has a hole with dimensions of 3 feet by 2 feet cut in it for a sink. What is the area of the kitchen counter that Carlos will laminate?. What is the area of a square that is 30 centimeters on one side? A 60 cm 2 B 120 cm 2 C 300 cm 2 D 900 cm 2 8. Writing to Explain If you know the perimeter of a rectangle but not its length or width, can you calculate its area? Explain. Topic 1 29

5 Area of Parallelograms and Triangles Reteaching 1-3 Find the area of this parallelogram. Find the area of this triangle. h 6 in. h 8 cm b 8 in. Use the formula A 5 bh. A A 5 48 sq in. The area of the parallelogram is 48 sq in. Use the formula A 5 1_ 2 bh. A 5 1_ A A 5 40 cm 2 b 10 cm The area of the triangle is 40 cm 2. Reteaching 1-3 Find the area of each parallelogram or triangle ft 8 m 50 ft 15 m 3. Triangle: b 5 6 ft, h 5 9 ft 4. Parallelogram: b 5 18 m, h 5 13 m 5. Triangle: b 5 20 in., h 5 9 in. 6. Writing to Explain Tony says he does not have enough information to find the area of this parallelogram. Is he correct? Explain cm.2 cm Topic 1 35

6 Area of Parallelograms and Triangles Find the area of each parallelogram or triangle Practice ft 18 cm 14 ft 12 cm Practice Triangle 4. Parallelogram 5. Triangle b 30 m b 18 in. b 20 ft h 15 m h 2 ft h 3 yd 6. Writing to Explain The area of a triangle is 42 square inches. The triangle s base is 6 inches. Find the height of the triangle. Explain how you do it.. Number Sense A parallelogram has a base of 4 m and a height of 3 m. Find the area of the parallelogram in square centimeters. 8. Estimation Which is the best estimate of the area of a triangle that has a base of cm and a height of 8.33 cm? A 200 cm 2 B 160 cm 2 C 100 cm 2 D 50 cm 2 9. Reasoning The area of a figure is 36 cm 2. Give 4 possible shapes of the figure. Where possible give 3 possible sets of dimensions for each possible shape. 36 Topic 1

7 Circumference Reteaching 1-4 Find the circumference. Use 3.14 or 22 for π. Use the formula C 2πr. C 2πr C C C m 8 m Find the diameter and the radius of a circle with a circumference of in. Reteaching 1-4 Divide by π to find the diameter. C πd, so π d C π d d = 21 in. To find the radius, divide the diameter by r = 10.5 in. Find each circumference. Use 22 or 3.14 for π m 14.4 ft 12.4 cm Find the missing measurements for each circle. Round to the nearest hundredth. 4. C ft. 5. C m 6. r 5.95 yd d = r = C =. Number Sense Which circle has the greater circumference: a circle with a diameter of 13.2 in., or a circle with a radius of 6.9 in.? Explain. 42 Topic 1

8 Circumference Find each circumference. Use 3.14 or 22 for π. Practice ft 12 cm m 13 in. Find the missing measurement for each circle. Round to the nearest hundredth. 5. C cm, d = 6. C m, r =. Estimation CD s have a diameter of about 5 in. Estimate the circumference of a CD. Practice Angela baked an apple pie that had a radius of 6 in. She wants to cut the pie into eight equal slices. How wide will each piece of pie be at the outer edge? A 5.2 in. B 4. in. C 4.4 in. D 4.2 in. 9. Writing to Explain Based on the diagram, is it correct to say that the smaller circle has one half the circumference of the larger. Why? Topic 1 43

9 Area of a Circle Reteaching 1-5 A circular bucket has a radius of 6 in. Find the area of the bottom of the bucket. The formula for finding the area of a circle is A r 2. One Way Another Way With a Calculator Use 3.14 for. Use 22 for. Press: A r 2 A r in in 2 Display: 6 x 2 The bucket s area is about 113 in 2. Find the area of each circle to the nearest whole number. Use 3.14 or 22 for cm m 5 4 in. Reteaching r 9 yd 5. d 20 m 6. r 14 cm. d 2.4 ft 8. r 22 cm 9. d 8.8 m 10. d 32 cm 11. r 5.3 m 12. Reasoning If the circumference of a circle is 18, what is the area of the circle? Topic 1 49

10 Area of a Circle Find the area of each circle to the nearest whole number. Use 3.14 or 22 for Practice in km 23. cm 4. d 14 in. 5. r cm 6. d 2 mi Practice 1-5 Brian s dad wants to put a circular pool in their backyard. He can choose between pools with diameters of 15 ft, 1 ft, or 22 ft. Round to the nearest square foot.. How many more square feet would the 1 ft pool use than the 15 ft pool? 8. How many more square feet would the 22 ft pool use than the 1 ft pool? 9. On a water ride at the amusement park, a rotating valve sprays water for 15 ft in all directions. What is the area of the circular wet patch it creates? A 30 ft 2 B 31.4 ft 2 C 94.2 ft 2 D 06.5 ft Writing to Explain Explain how to find the radius of a circle with an area of mi. 50 Topic 1