# How do you use Heron's formula to determine the area of a triangle with sides of that are 35, 58, and 41 units in length?

Jun 29, 2016

Area of triangle is $708.36$ square units.

#### Explanation:

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

The sides of triangle are $35$, $58$ and $41$ and hence

$s = \frac{1}{2} \left(35 + 58 + 41\right) = \frac{1}{2} \times 134 = 67$ and

Area of triangle is $\sqrt{67 \times \left(67 - 35\right) \times \left(67 - 58\right) \times \left(67 - 41\right)}$

= $\sqrt{67 \times 32 \times 9 \times 26}$

= $4 \times 3 \times \sqrt{67 \times 2 \times 26} = 12 \sqrt{3484} = 12 \times 59.03 = 708.36$ square units.