# How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 16, and 22 units in length?

Jan 13, 2016

A ≈ 120

#### Explanation:

Heron's formula is a two step process :

step 1 : Calculate half of the Perimeter (s )

If the lengths of the sides are a , b and c , then

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

In this question let a = 15 , b = 16 and c = 22

$\Rightarrow s = \frac{15 + 16 + 22}{2} = \frac{53}{2} = 26.5$

step 2 : Calculate Area (A ) using :

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

substitute in values :

 A = sqrt(26.5(26.5 - 15 )(26.5 -16 )(26.5 - 22 )

rArr A = sqrt(26.5 xx 11.5 xx 10.5 xx 4.5 ) = sqrt14399.4375 ≈ 120