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Area and Length, Page 6

Hero’s Formula

If you are given three sides of a triangle, you can use Hero’s Formula to find the area of the triangle. Hero’s Formula states that if you know the sides a, b, and c of a triangle, then the area K of the triangle can be found by: 

K = square root of [s(s - a)(s - b)(s - c)] where s = 1/2 * (a + b + c).

s is called the semi-perimeter.

Example:

Given triangle ABC with a = 23, b = 31, and c = 40, find the area of the triangle.

First find the semi-perimeter:

s = 1/2 * (a + b + c); s = 1/2 * (23+31+40); s = 47

Now you can use Hero’s Formula:

K = square root of [s(s - a)(s - b)(s - c)]; K = square root of [47(47 - 23)(47 - 31)(47 - 40)]; K = 355.4