# How do you find the area of a triangle given a=3, b=7, c=8?

Jul 10, 2015

Use Heron's formula to find the area of the triangle = $6 \sqrt{3}$

#### Explanation:

Given three sides of a triangle: $a , b , c$
and the semi-perimeter $s = \frac{a + b + c}{2}$

Heron's formula says that the area of the triangle can be calculated as:
$\textcolor{w h i t e}{\text{XXXX}}$$A = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

Given: $\textcolor{w h i t e}{\text{XXXX}}$$a = 3$$\textcolor{w h i t e}{\text{XXXX}}$$b = 7$$\textcolor{w h i t e}{\text{XXXX}}$$c = 8$
$\textcolor{w h i t e}{\text{XXXX}}$$s = 9$
and the area is
$\textcolor{w h i t e}{\text{XXXX}}$$A = \sqrt{9 \cdot 6 \cdot 2 \cdot 1}$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= \sqrt{108}$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= 6 \sqrt{3}$