# How do you use Heron's formula to find the area of a triangle with sides of lengths 3 , 5 , and 5 ?

Jan 27, 2016

${\text{Area}}_{\triangle} = \frac{7}{4} \sqrt{39}$

#### Explanation:

Given sides $\left(a , b , c\right) = \left(3 , 3 , 5\right)$
the semi-perimeter is $s = \frac{3 + 3 + 5}{2} = \frac{13}{2}$

and by Heron's formula: ${\text{Area}}_{\triangle} = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

So
color(white)("XXX")"Area"_triangle = sqrt(13/2xx7/2xx7/2xx3/2)

$\textcolor{w h i t e}{\text{XXXXXXX}} = \sqrt{\frac{13 \times 3 \times {7}^{2}}{{4}^{2}}}$

$\textcolor{w h i t e}{\text{XXXXXX}} = \frac{7}{4} \sqrt{39}$