1. Area of Triangles C a b A B c
Area = 1/2bc sinA or
Area = 1/2ac sinB or
Area = 1/2ab sinC
: To use this formula, you must know 2 sides & the angle between them (the angle formed by the 2 sides).

2. C b a A B 3.58 Ex: Find the area of the triangle to the nearest tenth.1. C
: To use this formula, you must know either a or b…this means we must use law of sines or law of cosines to find the missing sides. We can find a or b…it doesn’t matter. b
=3.5
73˚ a
37˚40’
69˚20’ A B
3.58
: We found C by taking
180-(sum of A+B).
Area = 1/2bc sinA
Area = 3.8 sq. units

3. C 12 5 A B 13 Ex: Find the area of the triangle to the nearest tenth.2. C
: We need to use the Law of Cosines to find one of the angles…it doesn’t matter which one.
You may notice that 5, 12, & 13 are pythagorean triples which means this is a right triangle…C=90˚
90˚ 12 5 A B 13
: We’ll pretend we didn’t
know it was a right triangle.
Area = 1/2ab sinC
Area = 30 sq. units

4. A 15 20 C B a Ex: Find the area of the triangle to the nearest tenth.3. A
: We know 2 sides & the angle between them, so we can simply use the area of a triangle formula.
115˚ 15 20 C B a
Area = 1/2bc sinA
Area = sq. units

5. Ex: Find the area of each circular segment to the nearest tenth,
given its central angle Ø, and the radius of the circle. 4.
: All radii of a circle are
equal…this means we
know 2 sides of a triangle
& the angle between them.
Area of
Area
of circular
segment
= Area of sector
“Plan of Attack”: Area of circular segment = Area of sector - Area of
Area = 1/2bc sinA
A =1/2 (7)(7)sin(π⁄8)
A = 9.376
Area of sector=πr2•[(π/8)/2π]
A=π•49•.0625
A≈9.621
Area of circular segment =
A≈.245 or .2
(to nearest tenth)