# How do you use Heron's formula to find the area of a triangle with sides of lengths 5 , 6 , and 7 ?

##### 1 Answer
Feb 1, 2016

$\text{A"=14.7 "square units}$ (rounded to one decimal place)

#### Explanation:

"A"=sqrt(s(s-a)(s-b)(s-c), where $s$ is the semiperimeter.

The semiperimeter is the perimeter divided by 2, $s = \frac{a + b + c}{2}$.

Let side $a = 5$, side $b = 6$, and side $c = 7$.

$s = \frac{5 + 6 + 7}{2}$

$s = \frac{18}{2}$

$s = 9$

Substitute the known values into Heron's formula.

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

"A"=sqrt(9(9-5)(9-6)(9-7)

Simplify.

$\text{A} = \sqrt{9 \left(4\right) \left(3\right) \left(2\right)}$

$\text{A} = \sqrt{216}$

$\text{A"=14.7 "square units}$ (rounded to one decimal place)