9.2 – The Area of a Triangle

Essential Question: Explain the two ways to find the area of a triangle.

Area of this triangle:

• K = bh2

1

h

b

a

C

B

A

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

,sina

hC

CabK sin2

1

The Area of a Triangle:

• The area K of ∆ABC is given by:

BacAbcCabK sin2

1sin

2

1sin

2

1

Example

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

Example

• Find the area of each triangle.

a.

b.

c.

30º

4

10

10

150º4

45º

2

5

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.

Example

• Find the area of the quadrilateral.

Segment of a circle:

Example

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

6

Example

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