# How do you use Heron's formula to find the area of a triangle with sides of lengths 2 , 2 , and 2 ?

Jan 24, 2016

$A = \sqrt{3} \approx 1.7321$

#### Explanation:

Heron's formula states that for a triangle with sides $a , b , c$ and a semiperimeter $s = \frac{a + b + c}{2}$, the area of the triangle is

$A = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

Here, we know that

$s = \frac{2 + 2 + 2}{2} = 3$

which gives an area of

$A = \sqrt{3 \left(3 - 2\right) \left(3 - 2\right) \left(3 - 2\right)}$

$A = \sqrt{3} \approx 1.7321$

This problem could also be solved by drawing the equilateral triangle and splitting it into two right triangles with base $1$ and height $\sqrt{3}$, giving each right triangle area $\frac{\sqrt{3}}{2}$ and the whole triangle an area of $\sqrt{3}$.