# How do you use Heron's formula to determine the area of a triangle with sides of that are 25, 18, and 22 units in length?

$192.642 \setminus \setminus {\textrm{u n i t}}^{2}$

#### Explanation:

Semi perimeter $s$ of triangle with the sides say $a = 25 , b = 18 , c = 22$ is given as

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

$= \setminus \frac{25 + 18 + 22}{2}$

$= 32.5$

Now, using Hero's formula, the area $\setminus \Delta$ of triangle is given as

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

$= \setminus \sqrt{32.5 \left(32.5 - 25\right) \left(32.5 - 18\right) \left(32.5 - 22\right)}$

$= 192.642 \setminus \setminus {\textrm{u n i t}}^{2}$