# How do you use Heron's formula to determine the area of a triangle with sides of that are 35, 28, and 41 units in length?

Apr 17, 2018

$483$ units squared

#### Explanation:

Heron's formula states that,

$A = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

• $s$ is the semiperimeter of the triangle, given by $s = \frac{a + b + c}{2}$.

• $a , b , c$ are the sides of the triangle

Let $a = 35 , b = 28 , c = 41$

$\therefore s = \frac{35 + 28 + 41}{2} = \frac{104}{2} = 52$

So, the area of this triangle will be:

$A = \sqrt{52 \left(52 - 35\right) \left(52 - 28\right) \left(52 - 41\right)}$

$= \sqrt{52 \cdot 17 \cdot 24 \cdot 11}$

$= \sqrt{233376}$

$\approx 483$

So, the area of the triangle will be $483$ units squared.