# A triangle has sides with lengths: 7, 2, and 15. How do you find the area of the triangle using Heron's formula?

Jul 31, 2016

$= 42.43$

#### Explanation:

As per Heron's formula
Area of a triangle with sides $a$;$b$; and $c$
$A = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$
where $s$ is half perimeter of the triangle and is given by
$s = \frac{a + b + c}{2}$
So we have
$a = 7$ ;$b = 2$ and $c = 15$
Therefore Perimeter of the triangle
$s = \frac{7 + 2 + 15}{2}$
or
$s = \frac{24}{2}$
or
$s = 12$
Area of the triangle
$A = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$
$= \sqrt{12 \left(12 - 7\right) \left(12 - 2\right) \left(12 - 15\right)}$
=sqrt(12(5)(10)(3)
$= \sqrt{1800}$
$= 42.43$