1. 9.2 – The Area of a Triangle Essential Question: Explain the two ways to find the area of a triangle.

2. Area of this triangle: K = h b a C B A

3. However, we can find the area of a Δ with 2 sides and the included angle: Using right triangle trigonometry, we know that so we can substitute a sin C for h. So

4. The Area of a Triangle: The area K of ∆ABC is given by:

5. Example Two sides of a Δ have lengths of 10 and 7 cm. The included angle is 43º. Find the area of the Δ.

6. Example Find the area of each triangle. a. b. c. 30º 4 10 150º 4 45º 2 5

7. Example The area of a Δ is 15 cm². If 2 of its sides are 12 and 5 cm, find the possible measures of <C.

8. Example Find the area of the quadrilateral.

9. Segment of a circle:

10. Example Find the area of a segment of a circle with radius 2 if the measure of the central angle of the segment is.

11. Example Find exact area of a regular hexagon inscribed in a unit circle. Then approximate the area to the nearest tenth.