# How do you use Heron's formula to find the area of a triangle with sides of lengths 3 , 7 , and 7 ?

Feb 28, 2016

The area is $\approx 10.3$ square units

#### Explanation:

Heron's formula is A=sqrt(s(s-a)(s-b)(s-c), where $A$ is the area, $s$ is the semi-perimeter, and $a , b , \mathmr{and} c$ are the sides of the triangle.

The semi-perimeter is half the perimeter, with the formula $s = \frac{a + b + c}{2}$.

Let
$a = 3$
$b = 7$
$c = 7$

Solution
Determine semi-perimeter, then substitute known values into Heron's formula and solve.

$s = \frac{3 + 7 + 7}{2}$

$s = \frac{17}{2}$

$s = 8.5$

$A = \sqrt{8.5 \left(8.5 - 3\right) \left(8.5 - 7\right) \left(8.5 - 7\right)}$

$A = \sqrt{8.5 \left(5.5\right) \left(1.5\right) \left(1.5\right)}$

$A = \sqrt{101.1875}$

$A = 10.3$ square units rounded to one decimal place