# How do you use Heron's formula to find the area of a triangle with sides of lengths 23 , 21 , and 7 ?

May 22, 2018

Area of triangle color(green)(A_t = 72.85 sq units

#### Explanation:

Given : $a = 23 , b = 21 , c = 7$

Heron’s formula for area of triangle

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

Semi perimeter $s = \frac{a + b + c}{2}$

$s = \frac{23 + 21 + 7}{2} = 25.5$

${A}_{t} = \sqrt{25.5 \cdot \left(25.5 - 23\right) \cdot \left(25.5 - 21\right) \cdot \left(25.5 - 7\right)}$

Area of triangle color(green)(A_t = 72.85 sq units