# How do you find the area of a triangle with a=15, b=17, c=10?

Oct 4, 2015

Use Heron's formula to get

#### Explanation:

Heron's formula for the area of a triangle with sides of length $a , b , c$ is
color(white)("XXX")A= sqrt(s(s-a)(s-b(s-c))
where $s$ is the semi-perimeter (that is, $\frac{a + b + c}{2}$)

Given $a = 15 , b = 17 , c = 10$
$s = 21$
and
$A = \sqrt{21 \cdot \left(21 - 15\right) \cdot \left(21 - 17\right) \cdot \left(21 - 10\right)}$

$\textcolor{w h i t e}{\text{XX}} = \sqrt{21 \cdot 6 \cdot 4 \cdot 11}$

$\textcolor{w h i t e}{\text{XX}} = \sqrt{5544}$

$\textcolor{w h i t e}{\text{XX}} \cong 74.46$