# How do you find the area given a=12, b=15, c=9?

May 25, 2017

Area $= 54$ sq. units

#### Explanation:

Assuming $a , b \mathmr{and} c$ are the three sides of a triangle we can apply Heron's formula to find the area.

Area=sqrt(p (p−a )(p− b)(p−c))
where p is half the perimeter, or $\frac{a + b + c}{2}$ (often called the semi-perimeter)

In this example: $a = 12 , b = 15 , c = 9$

$p = \frac{12 + 15 + 9}{2} = 18$

Area $= \sqrt{18 \left(18 - 12\right) \left(18 - 15\right) \left(18 - 9\right)}$

$= \sqrt{18 \times 6 \times 3 \times 9}$

$= \sqrt{2916}$

$= 54$ sq. units