1. 8-4 Area of Triangles and Trapezoids Learn to find the area of triangles and trapezoids.

2. 8-4 Area of Triangles and Trapezoids You can divide any parallelogram into two congruent triangles. So the area of each triangle is half the area of the parallelogram.

3. 8-4 Area of Triangles and Trapezoids

4. 8-4 Area of Triangles and Trapezoids Find the area of the triangle. Additional Example 1A: Finding the Area of a Triangle A = 1212 bh Write the formula. A = 1212 (20 · 12) Substitute 20 for b and 12 for h. A = 120 The area is 120 ft 2. A = 1212 (240) Multiply.

5. 8-4 Area of Triangles and Trapezoids An altitude of a triangle is a perpendicular segment from one vertex to the line containing the opposite side. The length of the altitude is the height. Reading Math

6. 8-4 Area of Triangles and Trapezoids Find the area of the triangle. Additional Example 1B: Finding the Area of a Triangle A = 1212 bh Write the formula. A = 1212 (30 · 24) Substitute 30 for b and 24 for h. A = 360 The area is 360 in 2. A = 1212 (720) Multiply.

7. 8-4 Area of Triangles and Trapezoids Find the area of the triangle. Check It Out: Example 1A A = 1212 bh Write the formula. A = 1212 (5 · 8) Substitute 5 for b and 8 for h. A = 20 The area is 20 in 2. A = 1212 (40) Multiply. 8 in. 5 in.

8. 8-4 Area of Triangles and Trapezoids Find the area of the triangle. Check It Out: Example 1B A = 1212 bh Write the formula. A = 54 The area is 54 in 2. A = 1212 (108) Multiply. 24 ft 4 ft 1 2 A = 1212 (4 24) 1 2 Substitute 4 for b and 24 for h. 1 2

9. 8-4 Area of Triangles and Trapezoids The diagram shows the section of a forest being studied. What is the area of the section? Additional Example 2: Application A = 1212 bh Write the formula. A = 1212 (43.9 16) Substitute 43.9 for b. Substitute 16 for h. A = 351.2 The area is 351.2 km 2. A = 1212 (702.4) Multiply.

10. 8-4 Area of Triangles and Trapezoids The diagram shows the section of a park being studied. What is the area of the section? Check It Out: Example 2 A = 1212 bh Write the formula. A = 1212 (48 · 24.5) Substitute 48 for b. Substitute 24.5 for h. A = 588 The area is 588 m 2. A = 1212 (1176) Multiply. 24.5 m 48 m

11. 8-4 Area of Triangles and Trapezoids

12. 8-4 Area of Triangles and Trapezoids Find the area of the trapezoid. Additional Example 3: Finding the Area of a Trapezoid A = 1212 h(b 1 + b 2 ) ‏ Use the formula. A = 53 The area is 53 yd 2. Multiply. A = 1212 · 4(26 ) ‏ 1 2 Substitute 4 for h, 14 for b 1, and 12 for b 2. 1 2 A = 1212 · 4(14 + 12 ) ‏ 1 2

13. 8-4 Area of Triangles and Trapezoids Find the area of the trapezoid. Check It Out: Example 3 A = 1212 h(b 1 + b 2 ) ‏ Use the formula. A = 1212 · 7(16 + 12) ‏ A = 1212 · 7(28) ‏ A = 98 The area is 98 cm 2. Substitute 7 for h, 16 for b 1, and 12 for b 2. Multiply. 12 cm 16 cm 7 cm