# How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 18, and 19 units in length?

Area $= 126.554 \text{ }$square units

#### Explanation:

Let the sides be $a = 15$ and $b = 18$ and $c = 19$

Solve for the half perimeter $s = \frac{a + b + c}{2} = \frac{15 + 18 + 19}{2} = 26$

The Heron's Formula for the area of the triangle

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

Area $= \sqrt{26 \left(26 - 15\right) \left(26 - 18\right) \left(26 - 19\right)}$

Area $= 126.554 \text{ }$square units

God bless....I hope the explanation is useful.

Mar 26, 2016

≈ 126.55 square units

#### Explanation:

This is a 2 step process.

step 1 : Calculate half the perimeter (s) of the triangle.

let a = 15 , b = 18 and c = 19

$s = \frac{a + b + c}{2} = \frac{15 + 18 + 19}{2} = \frac{52}{2} = 26$

step 2 : Calculate the area using

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

$= \sqrt{26 \left(26 - 15\right) \left(26 - 18\right) \left(26 - 19\right)}$

 = sqrt(26xx11xx8xx7) ≈ 126.55" square units "