1. Holt CA Course 1 10-1 Perimeter AF3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = bh, C =  d–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 California Standards 1212

2. Holt CA Course 1 10-1 Perimeter Vocabulary perimeter

3. Holt CA Course 1 10-1 Perimeter The perimeter of a polygon is the sum of the lengths of its sides.

4. Holt CA Course 1 10-1 Perimeter Additional Example 1: Finding the Perimeter of a Polygon Find the perimeter of the figure. 2.8 + 3.6 + 3.5 + 3 + 4.3 Add all the side lengths. The perimeter is 17.2 in.

5. Holt CA Course 1 10-1 Perimeter Check It Out! Example 1 Find the perimeter of the figure. 3.3 + 3.3 + 4.2 + 4.2 + 3 Add all the side lengths. 3.3 in. 4.2 in. 3 in. The perimeter is 18 in.

6. Holt CA Course 1 10-1 Perimeter

7. Holt CA Course 1 10-1 Perimeter Additional Example 2: Using a Formula to Find Perimeter Find the perimeter P of the parallelogram. P = 2l+ 2w Substitute 12 for l and 3 for w. P = (2 12) + (2 3) P = 24 + 6 P = 30 Multiply. Add. The perimeter is 30 cm. 12 cm 3 cm

8. Holt CA Course 1 10-1 Perimeter Check It Out! Example 2 Find the perimeter P of the parallelogram. P = 2l + 2w Substitute 15 for l and 2 for w. P = (2 15) + (2 2) P = 30 + 4 P = 34 Multiply. Add. The perimeter is 34 cm. 15 cm 2 cm

9. Holt CA Course 1 10-1 Perimeter A. What is the length of side a if the perimeter equals 1,471 mm? P = sum of side lengths Use the values you know. 1,471 = 416 + 272 + 201 + 289 + a 1,471 = 1,178 + a 1,471 – 1,178 = 1,178 + a – 1,178 Add the known lengths. Subtract 1,178 from both sides. 293 = a Side a is 293 mm long. Additional Example 3: Finding Unknown Side Lengths and the Perimeter of a Polygon Find each unknown measure.

10. Holt CA Course 1 10-1 Perimeter 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 P = 72 + 55 + 50 + 33 + 22 + 22 P = 254 Step 2: Find the perimeter. The perimeter of the polygon is 254 cm.

11. Holt CA Course 1 10-1 Perimeter l = 4w Find the length. l = (4 19) l = 76 Substitute 19 for w. Multiply. 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? 4w4w 19 cm

12. Holt CA Course 1 10-1 Perimeter Additional Example 3C Continued P = 2 l + 2 w Substitute 76 and 19. P = 2(76) + 2(19) P = 152 + 38 P = 190 Multiply. Add. Use the formula for the perimeter of a rectangle. The perimeter of the rectangle is 190 cm. 4w4w 19 cm

13. Holt CA Course 1 10-1 Perimeter Check It Out! Example 3 Find each unknown measure. A. What is the length of side a if the perimeter equals 1,302 mm? P = sum of side lengths Use the values you know. 1,302 = 212 + 280 + 250 + 240 + a 1,302 = 982 + a 1,302 – 982 = 982 + a – 982 Add the known lengths. Subtract 982 from both sides. 320 = a Side a is 320 mm long. 212 mm 280 mm a 250 mm 240 mm

14. Holt CA Course 1 10-1 Perimeter P = 14 + 12 + 8 + 4 + 6 + 16 P = 60 The perimeter of the polygon is 60 m. Check It Out! Example 3 Find each unknown measure. B. What is the perimeter of the polygon? 12 m 14 m b m 8 m 6 m 4 m 16 m Step 1: Find b. Find the sum of the lengths opposite side b. b = 12 + 4 b = 16 Step 2: Find the perimeter.

15. Holt CA Course 1 10-1 Perimeter l = 5w Find the length. l = (5 13) l = 65 Substitute 13 for w. Multiply. 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? 5w5w 13 cm

16. Holt CA Course 1 10-1 Perimeter Check It Out! Example 3C Continued 65 cm 13 cm P = 2 l + 2 w Substitute 65 and 13. P = 2(65) + 2(13) P = 130 + 26 P = 156 Multiply. Add. Use the formula for the perimeter of a rectangle. The perimeter of the rectangle is 156 cm.