Question

How do you use Heron's formula to find the area of a triangle with sides of lengths `3`, `5`, and `7`?

Answer 1

First, I like to start by writing out the formula:
A = `sqrt(s*(s-1)(s-b)(s-c))`, where s = semiperimeter, and a, b, and c are the sides of the triangle.

Explanation:

First, perimeter: 3 + 5 + 7 = 15
Then, semiperimeter: `15/2` or 7.5

Now, Area = `sqrt(7.5(7.5-3)(7.5-5)(7.5-7))`
or about 6.495 square units.