1. Holt CA Course 1 10-4 Area of Triangles and Trapezoids 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: AF1.2, AF3.2 California Standards 1212

2. Holt CA Course 1 10-4 Area of Triangles and Trapezoids

3. Holt CA Course 1 10-4 Area of Triangles and Trapezoids A. Find the area of the triangle. Teacher Example 1A: Finding the Area of a Triangle 5 8 A = 1212 bh Use the formula. A = 1212 (8 · 5) Substitute 8 for b and 5 for h. A = 20 The area of the triangle is 20 square units.

4. Holt CA Course 1 10-4 Area of Triangles and Trapezoids B. Find the area of the triangle. Teacher Example 1B: Finding the Area of a Triangle 9 A = 1212 bh Use the formula. A = 1212 (12 · 9) Substitute 12 for b and 9 for h. A = 54 The area of the triangle is 54 square units. 12

5. Holt CA Course 1 10-4 Area of Triangles and Trapezoids A. Find the area of the triangle. A = 1212 bh Use the formula. A = 1212 (6 · 9) Substitute 6 for b and 9 for h. A = 27 The area of the triangle is 27 square units. Student Practice 1A: 6 9

6. Holt CA Course 1 10-4 Area of Triangles and Trapezoids B. Find the area of the triangle. A = 1212 bh Use the formula. A = 1212 (7 · 10) Substitute 7 for b and 10 for h. A = 35 The area of the triangle is 35 square units. Student Practice 1B: 10 7

7. Holt CA Course 1 10-4 Area of Triangles and Trapezoids The two parallel sides of a trapezoid are its bases, b 1 and b 2. The height of a trapezoid is the perpendicular distance between the bases. h b1b1 b2b2

8. Holt CA Course 1 10-4 Area of Triangles and Trapezoids In the term b 1, the number 1 is called a subscript. It is read as “b-one” or “b sub-one.” Reading Math

9. Holt CA Course 1 10-4 Area of Triangles and Trapezoids A. Find the area of the trapezoid. Teacher Example 2A: Finding the Area of a Trapezoid 5 in. 6 in. 9 in. A = 1212 h(b 1 + b 2 ) Use the formula. A = 1212 · 6(9 + 5) A = 1212 · 6(14) A = 42 The area of the trapezoid is 42 in 2. Substitute. Multiply. Add.

10. Holt CA Course 1 10-4 Area of Triangles and Trapezoids B. Find the area of the trapezoid. Teacher Example 2B: Finding the Area of a Trapezoid A = 1212 h(b 1 + b 2 ) Use the formula. A = 1212 · 7(16 + 12) A = 1212 · 7(28) A = 98 The area of the trapezoid is 98 cm 2. Substitute. Multiply. Add. 12 cm 16 cm 7 cm

11. Holt CA Course 1 10-4 Area of Triangles and Trapezoids A. Find the area of the trapezoid. A = 1212 h(b 1 + b 2 ) Use the formula. A = 1212 · 6(11 + 4) A = 1212 · 6(15) A = 45 The area of the trapezoid is 45 in 2. Substitute. Multiply. Add. Student Practice 2A: 4 in. 6 in. 11 in.

12. Holt CA Course 1 10-4 Area of Triangles and Trapezoids B. Find the area of the trapezoid. A = 1212 h(b 1 + b 2 ) Use the formula. A = 1212 · 9(5 + 16) A = 1212 · 9(21) A = 94.5 The area of the trapezoid is 94.5 cm 2. Substitute. Multiply. Add. Student Practice 2B: 16 cm 5 cm 9 cm

13. Holt CA Course 1 10-4 Area of Triangles and Trapezoids The state of Wisconsin is shaped somewhat like a trapezoid. What is the approximate area of the state? Teacher Example 3: Geometry Application A = 1212 h(b 1 + b 2 ) Use the formula. A = 1212 · 300(153 + 220) A = 1212 · 300(373) A = 55,950 The area of Wisconsin is approximately 56,000 square miles. Substitute. Multiply. Add.

14. Holt CA Course 1 10-4 Area of Triangles and Trapezoids A large preserve has a similar trapezoid shape. What is the approximate area of the preserve? Student Practice 3: 232 mi 116 mi A = 1212 h(b 1 + b 2 ) Use the formula. A = 1212 · 129(232 + 116) A = 1212 · 129(348) A = 22,446 The area of the preserve is approximately 22,446 square miles. Substitute. Multiply. Add. 129 mi

15. Holt CA Course 1 10-4 Area of Triangles and Trapezoids Lesson Quiz Find the area of each figure. 1. 3. 9 in 2 45 ft 2 60 ft 2 87.5 ft 2 2. 4. 4. What is the height of a triangle with area 36 cm 2 and a base 9 cm? 8 cm