# How do you use Heron's formula to determine the area of a triangle with sides of that are 25, 29, and 32 units in length?

Jan 11, 2016

$A = \text{345 square units}$

#### Explanation:

Heron's formula is $A = \sqrt{\left(s\right) \left(s - a\right) \left(s - b\right) \left(s - c\right)}$, where $A$ is the area, $s$ is the semiperimeter, and $a , b , \mathmr{and} c$ are the sides of the triangle.

Let side $a = 25$.
Let side $b = 29$.
Let side $c = 32$.

Semiperimeter
The formula for the semiperimeter is $s = \frac{a + b + c}{2}$.

$s = \frac{25 + 29 + 32}{2}$

$s = \frac{86}{2}$

$s = 43$

Heron's Formula

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

A=sqrt(43(43-25)(43-29)(43-32)

$A = \sqrt{119196}$

$A = \text{345 square units}$