COMPACTED MATHEMATICS CHAPTER 10 AREA AND PERIMETER TOPICS COVERED:
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1 COMPACTED MATHEMATICS CHAPTER 10 AREA AND PERIMETER TOPICS COVERED: Perimeter of polygons Area of rectangles and squares Area of parallelograms Area of triangles Area of trapezoids
2 Activity 10-1 Perimeter NAME: Perimeter: The distance around the outside of a figure. Per means around. Meter means measure. Thus, the perimeter of a figure is the measure around it. Classify each shape by giving the most specific name possible. Then find the perimeter of each figure cm 10 cm 14 ft 14 ft 3.5 m 5 m 18 cm 9 ft 8.5 m.0 km m 6..9 km 0.9 m 0.9 m.4 km 1.8 m 1.6 km 0.9 m Regular polygon.5 km 1.8 m 4 in Find the perimeter of each rectangle. 1.5 ft cm 5 ft 60 cm 8. m 15 m Find the perimeter of each rectangle. 10. L = 48 mm W = 3 mm 11. L = 6. km W = 4.7 km 1. L = 1 in. W = 1 in. 13. Find the perimeter of a sheet of typing paper 8.5 in. wide and 11 in. long. 14. How many feet of border are needed to go around a square bulletin board that is 4.5 ft. on each side? 15. Find the perimeter of your bedroom. 16. Find the perimeter of your house. 17. Find the perimeter of your backyard.
3 Activity 10- Area of Parallelograms NAME: Formula for the area of a parallelogram: A bh Example: 8 m 5 m The height is measured straight up from the base. The height of this parallelogram is. A bh A 84 A 3 m. Find the perimeter and the area of each parallelogram. For the area, show all steps ft 10 ft 16 ft 15 m 16 m 1 m cm 3.6 cm 5.1 cm 6.5 cm 9.3 cm 6.5 cm ft 90 ft.0 m 1.8 m 100 ft 0.7 m The base of a parallelogram is 10 in. The height is in. more than half the base. Find the area. The height of a parallelogram is 4.5 cm. The base is twice the height. What is the area? The area of a parallelogram is 60 ft. The height is 5 ft. How long is the base? The area of a parallelogram is 75 cm. The base is 5 cm. Find the height.
4 Activity 10-3 Area of Triangles NAME: Formula for the area of a triangle: bh 1 A or bh (Half of the formula for a parallelogram.) Example: 5 in 6 in The height is measured straight up from the base. The height of this triangle is 5 in. bh A 65 A A 15 in. Find the area of each triangle using the formula above. Show all steps on a separate sheet of paper mm. 3 mm 7.5 cm 18 cm in. 7 m 1 in. 3 m in. 4 ft. 7 in. 4 ft km yd. 1 yd. 19 km 11. km. 3.7 km.
5 Activity 10-4 Area of Triangles NAME: Find the area of each triangle using the formula above. Show all steps on a separate sheet of paper mm. 1 yd 8 mm 1 yd cm 18 in 0 cm 16 in 5. 8 ft in 17 ft. 7 in 9 cm cm.5 in 6 in m 15 m 4.5 km 1.4 km A triangular sail has a base of 5 m and a height of 10 m. If canvas costs $18 a square meter, find the cost of canvas to make the sail. A square dinner napkin 8 in. on each side is folded along its diagonal. Find the area of the folder napkin.
6 Activity 10-5 Area of Trapezoids NAME: A trapezoid is a quadrilateral with only one pair of parallel sides. For determining its area one can start with the formula for a parallelogram: A bh. However with a trapezoid the top and bottom bases are different lengths. Thus, to find the area average the two bases and then multiply times the height. 1 1 Formula for the area of a trapezoid: A ( b1 b ) h [ ( 1 ) b b is just the average of the two bases.] 1 in 1 Example: A ( b1b ) h 6 in A 1 (1 15)6 15 in 1 A (7) 6 The two bases are always parallel to each other. A 81 in. Find the area of each trapezoid using the formula above. Show all steps on a separate sheet of paper. Trapezoid A z Trapezoid B z x x y y Trapezoid C z Trapezoid D x z y y x Trapezoid A 1. x=14 cm, y=6.5 cm, z=1 cm. x=4 cm, y=10 cm, z=5 cm 3. x=40 m, y=50 m, z=0 m 4. x=7 ft, y=15 ft, z=7 ft Trapezoid B 5. x=41 cm, y=78 cm, z= cm 6. x=6 cm, y=5 cm, z=18 cm 7. x=9 m, y=3 m, z=6 m 8. x=5 cm, y=70 cm, z=30 cm Trapezoid C 9. x=7 km, y=15.7 km, z=7 km 10. x=1.7 ft, y=9 ft, z=4.5 ft 11. x=1.6 cm, y=3. cm, z=1.4 cm Trapezoid D 1. x=6 in, y=16 in, z=9 in 13. x=41 cm, y=78 cm, z= cm 14. x=.8 m, y=.5 m, z=1.5 m
7 Activity Area of Different Shapes NAME: Find the area of each figure m 6 m m m 6 m in 3 m m 6 in 8 in 10 in 1 in in 1 in 7 in 10 cm 9 cm 18 cm 5 cm Find the area of the shaded region in each figure. 7. yard with a sandbox 8. wall with windows 9. sidewalk around pool Yard 15 ft by 0 ft Sandbox 6 ft by 7 ft Wall 8 ft by 16 ft Both windows 5 ft by 4 ft Sidewalk 30 ft by 30 ft Pool 7 ft by 7 ft 10. A bedroom is 15 ft long and 1 ft wide. How much will it cost to carpet the room if carpeting costs $ per square yard? (1 yd = 3 ft) 11. A rose garden in the city park is rectangular and is 9 m wide. If the area of the rectangle is 14, what is the length of the garden?
8 Activity 10-6 Which Measure Is It? NAME: PART 1 Use graph paper for all drawings. 1. Draw a figure whose perimeter is 4 units.. Draw a different figure whose perimeter is also 4 units. 3. Draw a figure whose area is 4 square units. 4. Draw a different figure whose area is also 4 square units. 5. Make up a real world word problem in which you need to find the perimeter of any quadrilateral. 6. Make up a real world word problem in which you need to find the area of any quadrilateral. 7. Can two different figures have the same area but different perimeters? Explain your answer. 8. Your dog, Benji, needs a new play area. You are in charge of building a fence around the dog s play area so that he can t run away. You are given 80 feet of fencing to build your play area. Build two different play areas that you think would be suitable for a dog using all of the fencing. For each of the drawings: A. Calculate the perimeter B. Calculate the area C. Explain in the space below why/how you chose the shape for each play area PART in. The perimeter of the rectangle is 6 in. Find the length of each side.. Amanda bought 40 metes of fencing to make an enclosure for her dog, Sushi. If Amanda expects a rectangular enclosure, what is the largest area it can have? Explain your answer. 3. The width of a rectangle is 4.5 inches and its perimeter is 31 inches. What is the length of the rectangle?
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