Question

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

Answer 1

Answer:

Use Heron's formula; see below.

Step-by-step explanation:

Use Heron's formula.

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

$s = \dfrac{a + b + c}{2}$

$area = \sqrt{s(s - a)(s - b)(s - c)}$

Example:

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

Find the area of the triangle.

$s = \dfrac{a + b + c}{2}$

$s = \dfrac{3 + 4 + 5}{2}$

$s = 6$

$area = \sqrt{s(s - a)(s - b)(s - c)}$

$area = \sqrt{6(6 - 3)(6 - 4)(6 - 5)}$

$area = \sqrt{6(3)(2)(1)}$

$area = \sqrt{36}$

$area = 6$