# How do you use Heron's formula to determine the area of a triangle with sides of that are 7, 15, and 9 units in length?

Feb 13, 2016

Area $\approx 43.39$ sq. units.

#### Explanation:

Heron's formula tells us that the area of a triangle with sides $a , b , \mathmr{and} c$ is
color(white)("XXX")"Area"_triangle=sqrt(s(s-a)(s-b)(s-c))
where $s$ is the semi-perimter ($\frac{a + b + c}{2}$).

In this case we have
$\textcolor{w h i t e}{\text{XXX")a=7 color(white)("XX")b=15 color(white)("XX")c=9 and color(white)("XX}} s = \frac{31}{2}$

So
Area"_triangle = sqrt(31/2xx17/2xx1/2xx13/2)

$\textcolor{w h i t e}{\text{XXXX}} \approx 41.39$