# How do you use Heron's formula to determine the area of a triangle with sides of that are 25, 28, and 31 units in length?

Dec 26, 2015

Substitute the values into Heron's formula to find:

$A = \sqrt{109956} \approx 331.59614$

#### Explanation:

Heron's formula can be written:

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

where $A$ is the area, $a$, $b$, $c$ are the lengths of the sides and

$s p = \frac{a + b + c}{2} \textcolor{w h i t e}{X}$ is the semi-perimeter.

In our example, $a = 25$, $b = 28$, $c = 31$

$s p = \frac{a + b + c}{2} = \frac{25 + 28 + 31}{2} = \frac{84}{2} = 42$

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

$= \sqrt{42 \left(42 - 25\right) \left(42 - 28\right) \left(42 - 31\right)}$

$= \sqrt{42 \cdot 17 \cdot 14 \cdot 11}$

$= \sqrt{109956} \approx 331.59614$