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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.