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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. 2 3. 18. or. 56 3. Warm Up Find each product. 1. 8  12 2. 3 3. 9.4  6.3 4. 3.5  7. 96. 1 3. 1 2.  5. 59.22. 24.5. California Standards.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. 2 3 18 or 56 3 Warm Up Find each product. 1.8  12 2. 3 3. 9.4  6.3 4. 3.5  7 96 1 3 1 2  5 59.22 24.5

  3. California Standards AF3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = bh, C = pd–the formulas for the perimeter of a rectangle,the area of a triangle, and the circumference of a circle, respectively). Also covered:NS2.1, AF1.1, AF2.1, AF3.2 1 2

  4. Vocabulary area base height

  5. h b The area of a figure is the number of non-overlapping unit squares needed to cover the figure. Area is measured in square units. Area = 15 square units The base of a parallelogram is the length of one side. Its height is the perpendicular distance from the base to the opposite side. For a rectangle, the base is the same as the length, and the height is the same as the width.

  6. Additional Example 1: Finding the Area of a Parallelogram Find the area of the parallelogram. A = bh Use the formula. Substitute for b and h. A = 16 · 8 8 m Multiply. A = 128 16 m The area of the parallelogram is 128 m2.

  7. Additional Example 2: Finding the Area of a Rectangle Find the area of the rectangle. 4.5 in. 7.4 in. A = lw Use the formula. Substitute for l and w. A = 7.4 · 4.5 Multiply. A = 33.3 The area of the rectangle is 33.3 in2.

  8. Additional Example 3: Finding Length or Width of a Rectangle The area of a playing field is 1,470 ft2 and the length is 42 ft. What is the width of the field? Use the formula for the area of a rectangle. A = lw 1,470 = 42 · w Substitute 1,470 for A and 42 for l. 1,470 42 42 · w 42 = Divide both sides by 42 to isolate w. 35 = w The width of the playing field is 35 ft.

  9. 4 yd 5 yd Additional Example 4: Measurement Application A carpenter is laying a wood floor measuring 4 yd by 5 yd. How many square feet of flooring material does she need? Step 1: Draw and label a diagram. Step 2: Convert the units. The wood floor is measured is yards, but the answer should be in feet. 3 ft 1 yd 4 yd · = 12 ft Convert yards to feet by multiplying by a ratio equal to 1. 3 ft 1 yd 5 yd · = 15 ft

  10. Additional Example 4 Continued A carpenter is laying a wood floor measuring 4 yd by 5 yd. How many square feet of flooring material does she need? Step 3: Find the area of the floor in square feet. A = lw Use the formula for the area of a rectangle. A = 12 · 15 Substitute 12 for l and 15 for w. A = 180 Multiply. The carpenter needs 180 ft2 of flooring material.

  11. Check It Out! Example 1 Find the area of the parallelogram. A = bh Use the formula. Substitute for b and h. A = 12 · 6 6 cm Multiply. A = 72 12 cm The area of the parallelogram is 72 cm2.

  12. Check It Out! Example 2 Find the area of the rectangle. 6.3 in. 8.2 in. A = lw Use the formula. Substitute for l and w. A = 8.2 · 6.3 Multiply. A = 51.66 The area of the rectangle is 51.66 in2.

  13. Check It Out! Example 3 The area of a rectangular parking lot is 3,570 ft2 and the width is 70 ft. What is the length of the parking lot? Use the formula for the area of a rectangle. A = lw 3,570 = l· 70 Substitute 3,570 for A and 70 for w. 3,570 70 l· 70 70 = Divide both sides by 70 to isolate l. 51 = l The length of the parking lot is 51 ft.

  14. Check It Out! Example 4 A carpenter is laying a tile floor measuring 5 yd by 7 yd. How many square feet of tile material does she need? 5 yd Step 1: Draw and label a diagram. 7 yd Step 2: Convert the units. The tile floor is measured is yards, but the answer should be in feet. 3 ft 1 yd 5 yd · = 15 ft Convert yards to feet by multiplying by a ratio equal to 1. 3 ft 1 yd 7 yd · = 21 ft

  15. Check It Out! Example 4 Continued A carpenter is laying a tile floor measuring 5 yd by 7 yd. How many square feet of tile material does she need? Step 3: Find the area of the tile floor in square feet. A = lw Use the formula for the area of a rectangle. A = 15 · 21 Substitute 15 for l and 21 for w. A = 315 Multiply. The carpenter needs 315 ft2 of tile material.

  16. 105 8 1 8 in2 or 13 57 2 or 1 2 ft2 28 Lesson Quiz: Part I Find the area of each figure. 1. 2. 3. 24.5 ft2 4. 84 ft2

  17. Lesson Quiz: Part II 5. Diego is building a rectangular platform measuring 36 in. by 54 in. What is the area of the platform in square feet? 13.5 ft2

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