Question

How do you find the area of a triangle when given only the lengths of three sides?

Answer 1

Use Heron's formula; see below.

Explanation:

Use Heron's formula.

Let the sides of the triangle have lengths a, b, and c.

`s = (a + b + c)/(2)`

`area = √(s(s - a)(s - b)(s - c))`

Example:

A triangle has side lengths 3, 4, and 5 units.

Find the area of the triangle.

`s = (a + b + c)/(2)`

`s = (3 + 4 + 5)/(2)`

`s = 6`

`area = √(s(s - a)(s - b)(s - c))`

`area = √(6(6 - 3)(6 - 4)(6 - 5))`

`area = √(6(3)(2)(1))`

`area = √(36)`

`area = 6`