# A triangle has sides with lengths: 7, 12, and 15. How do you find the area of the triangle using Heron's formula?

Jan 6, 2016

41.23 (2 decimal places )

#### Explanation:

this is a two step process

where a , b and c represent the three sides of the triangle

$\textcolor{red}{s t e p 1}$

calculate s (half of the triangles perimeter ) : $s = \frac{a + b + c}{2}$

in this case $s = \frac{7 + 12 + 15}{2} = \frac{34}{2} = 17$

$\textcolor{red}{s t e p 2}$

calculate area :  A = sqrt( s(s - a )(s - b )(s - c )

in this case A =  sqrt( 17(17 - 7 )(17 - 12 )(17 - 15 )

 rArr A = sqrt (17 xx 10 xx 5 xx 2 )= sqrt1700) = 41.23