# How do you use Heron's formula to find the area of a triangle with sides of lengths 14 , 8 , and 11 ?

Apr 19, 2016

Area of triangle is $87.83$

#### Explanation:

According to Heron's formula, area of a triangle whose three sides are $a$, $b$ and $c$ is given by $\sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$, where $s = \frac{1}{2} \left(a + b + c\right)$.

As in given case three sides are $14$, $8$ and $11$, $s = \frac{1}{2} \left(14 + 8 + 11\right) = \frac{33}{2}$ and hence area of the triangle is

$\sqrt{\frac{33}{2} \times \left(\frac{33}{2} - 14\right) \times \left(\frac{33}{2} - 8\right) \times \left(\frac{33}{2} - 11\right)}$

= $\sqrt{\frac{33}{2} \times \frac{5}{2} \times \frac{17}{2} \times \frac{11}{2}}$

= $\frac{1}{2} \sqrt{11 \times 3 \times 5 \times 17 \times 11} = \frac{11}{2} \sqrt{15 \times 17}$

= $\frac{11}{2} \sqrt{255} = \frac{11}{2} \times 15.969 = 87.83$