# How do you use Heron's formula to find the area of a triangle with sides of lengths 2 , 7 , and 7 ?

Jan 21, 2016

$4 \sqrt{3}$

#### Explanation:

In order to use Heron's formula, we will have to know the semiperimeter of the triangle. The semiperimeter is simply one half the perimeter of the triangle, so the semiperimeter $s$ of a triangle with sides $a , b , c$ can be expressed as

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

Thus, our current semiperimeter is

$s = \frac{2 + 7 + 7}{2} = 8$

Now, we can apply Heron's formula, which states that the area $A$ of a triangle can be found through

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

We know that $s = 8 , a = 2 , b = 7 , c = 7$, so

$A = \sqrt{8 \left(8 - 2\right) \left(8 - 7\right) \left(8 - 7\right)}$

$A = \sqrt{48}$

$A = 4 \sqrt{3}$