Area of Triangles Section 5.6

The Area of a Triangle Using Trigonometry Therefore, we can find the area of a triangle if we are given any two sides of a triangle and the measure of the included angle. (SAS)

Example Find the area of a regular octagon inscribed inside a circle of radius 9 inches.

Area of a Triangle Given Three Sides There is another way to determine the area of a triangle given all three sides. (SSS) If a, b, and c are the sides of a triangle the area (K) is given by the formula: where S = the semiperimeter of the triangle. This formula is named after the mathematician who derived it: Heron

Example Find the area of a triangle with sides 13, 15, 18.

The bases on a baseball diamond are 90 feet apart, and the front edge of the pitcher’s rubber is 60.5 feet from the back corner of home plate. Find the distance from the center of the front edge of the pitcher’s rubber to the far corner of first base.