# A triangle has sides with lengths: 16, 11, and 9. How do you find the area of the triangle using Heron's formula?

Jan 9, 2016

sqrt2268 ≈ 47.62

#### Explanation:

Using Heron's formula is a two step process.

step 1 : find half of the triangles perimeter (s)

label the lengths of the 3 sides a , b and c.
In this case a = 16 , b = 11 and c = 9.

$s = \frac{a + b + c}{2} = \frac{16 + 11 + 9}{2} = \frac{36}{2} = 18$

step 2 : Calculate the Area (A) using :

 A = sqrt (s(s - a )(s - b )(s - c )

$\Rightarrow \sqrt{18 \left(18 - 16\right) \left(18 - 11\right) \left(18 - 9\right)} = \sqrt{18 \times 2 \times 7 \times 9}$

 rArr A = sqrt2268 ≈47.62