# How do you use Heron's formula to find the area of a triangle with sides of lengths 4 , 5 , and 7 ?

##### 1 Answer
Apr 19, 2016

Area of the triangle is $7.483$

#### 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 $4$, $5$ and $7$, $s = \frac{1}{2} \left(4 + 5 + 7\right) = \frac{16}{2} = 8$ and hence area of the triangle is

$\sqrt{8 \times \left(8 - 4\right) \times \left(8 - 5\right) \times \left(8 - 7\right)} = \sqrt{8 \times 4 \times 3 \times 1} = \sqrt{56} = 7.483$