# How do you use Heron's formula to determine the area of a triangle with sides of that are 28, 29, and 32 units in length?

##### 1 Answer
May 2, 2016

Area of triangle is $377.175$ units

#### Explanation:

If the three sides of a triangle are $a$, $b$ and $c$, according to Heron's formula, area of triangle is given by

$\sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$ where $s = \frac{1}{2} \left(a + b + c\right)$

Here the three sides are $28$, $29$ and $32$ and hence

$s = \frac{1}{2} \left(28 + 29 + 32\right) = \frac{89}{2}$

Hence area of triangle is

sqrt(89/2xx(89/2-28)xx(89/2-29)xx(89/2-32)

or =$\sqrt{\frac{89}{2} \times \frac{33}{2} \times \frac{31}{2} \times \frac{25}{2}}$

or $\frac{5}{4} \sqrt{89 \times 33 \times 31} = \frac{5}{4} \sqrt{91047} = \frac{5}{4} \times 301.74 = 377.175$ units.