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AF3.1 Use variables in expressions describing geometric quantities (e.g.,

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

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AF3.1 Use variables in expressions describing geometric quantities (e.g.,

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  1. 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:AF1.1, AF1.2, AF3.2 1 2

  2. Vocabulary perimeter

  3. The perimeter of a polygon is the sum of the lengths of its sides.

  4. Additional Example 1: Finding the Perimeter of a Polygon Find the perimeter of the figure. Add all the side lengths. 2.8 + 3.6 + 3.5 + 3 + 4.3 The perimeter is 17.2 in.

  5. Check It Out! Example 1 Find the perimeter of the figure. 3.3 in. 3.3 in. Add all the side lengths. 3.3 + 3.3 + 4.2 + 4.2 + 3 The perimeter is 18 in. 4.2 in. 4.2 in. 3 in.

  6. Additional Example 2: Using a Formula to Find Perimeter Find the perimeter P of the parallelogram. 12 cm 3 cm P = 2l+ 2w Substitute 12 for l and 3 for w. P = (2 • 12) + (2 • 3) P = 24 + 6 Multiply. P = 30 Add. The perimeter is 30 cm.

  7. Check It Out! Example 2 Find the perimeter P of the parallelogram. 15 cm 2 cm P = 2l + 2w P = (2 •15) + (2 •2) Substitute 15 for l and 2 for w. P = 30 + 4 Multiply. P = 34 Add. The perimeter is 34 cm.

  8. Additional Example 3: Finding Unknown Side Lengths and the Perimeter of a Polygon Find each unknown measure. A. What is the length of side a if the perimeter equals 1,471 mm? P = sum of side lengths 1,471 = 416 + 272 + 201 + 289 + a Use the values you know. Add the known lengths. 1,471 = 1,178 + a 1,471 – 1,178 = 1,178 + a– 1,178 Subtract 1,178 from both sides. 293 = a Side a is 293 mm long.

  9. Additional Example 3: Finding Unknown Side Lengths and the Perimeter of a Polygon Find each unknown measure. B. What is the perimeter of the polygon? Step 1: Find b. Find the sum of the lengths opposite side b. b = 50 + 22 b = 72 Step 2: Find the perimeter. P = 72 + 55 + 50 + 33 + 22 + 22 P = 254 The perimeter of the polygon is 254 cm.

  10. Additional Example 3: Finding Unknown Side Lengths and the Perimeter of a Polygon C. The width of a rectangle is 19 cm. What is the perimeter of the rectangle if the length is 4 times the width? 4w 19 cm Find the length. l= 4w l = (4 •19) Substitute 19 for w. Multiply. l = 76

  11. Additional Example 3C Continued 4w 19 cm Use the formula for the perimeter of a rectangle. P = 2l + 2w Substitute 76and 19. P = 2(76) + 2(19) P = 152 + 38 Multiply. P = 190 Add. The perimeter of the rectangle is 190 cm.

  12. Check It Out! Example 3 Find each unknown measure. A. What is the length of side a if the perimeter equals 1,302 mm? 280 mm 212 mm 250 mm a P = sum of side lengths 240 mm 1,302 = 212 + 280 + 250 + 240 + a Use the values you know. Add the known lengths. 1,302 = 982 + a 1,302 – 982 = 982 + a– 982 Subtract 982 from both sides. 320 = a Side a is 320 mm long.

  13. Check It Out! Example 3 Find each unknown measure. B. What is the perimeter of the polygon? 12 m Step 1: Find b. 8 m Find the sum of the lengths opposite side b. b = 12 + 4 14 m 4 m b = 16 6 m Step 2: Find the perimeter. 16 m b m P = 14 + 12 + 8 + 4 + 6 + 16 P = 60 The perimeter of the polygon is 60 m.

  14. Check It Out! Example 3 C. The width of a rectangle is 13 cm. What is the perimeter of the rectangle if the length is 5 times the width? 5w 13 cm Find the length. l = 5w l = (5 •13) Substitute 13 for w. Multiply. l = 65

  15. Check It Out! Example 3C Continued 65 cm 13 cm Use the formula for the perimeter of a rectangle. P = 2l + 2w Substitute 65and 13. P = 2(65) + 2(13) P = 130 + 26 Multiply. P = 156 Add. The perimeter of the rectangle is 156 cm.

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