1. 17
Area of a Triangle

2. Theorem The area A of a triangle is
where b is the base and h is the altitude drawn to that base.
Use when you know the base and the height.

3. What if we are not given the base and
the height?
Suppose we know two sides a and b along with the included angle γ.
We can derive a formula for area of the triangle by noting the following.

5. Theorem
The area A of a triangle equals one-half the product of two of its sides times the sine of its included angle.

7. Theorem Heron’s Formula
What if we know three sides of a triangle?
Theorem Heron’s Formula
The area A of a triangle with sides a, b, and c is

8. Find the area of a triangle whose sides are 5, 8, and 11.
Let a =5, b =8, c =11.