# How do you use Heron's formula to find the area of a triangle with sides of lengths 2 , 2 , and 3 ?

Jan 22, 2016

$A r e a = 1.9843$ square units

#### Explanation:

Hero's formula for finding area of the triangle is given by
$A r e a = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

Where $s$ is the semi perimeter and is defined as
$s = \frac{a + b + c}{2}$

and $a , b , c$ are the lengths of the three sides of the triangle.

Here let $a = 2 , b = 2$ and $c = 3$

$\implies s = \frac{2 + 2 + 3}{2} = \frac{7}{2} = 3.5$

$\implies s = 3.5$

$\implies s - a = 3.5 - 2 = 1.5 , s - b = 3.5 - 2 = 1.5 \mathmr{and} s - c = 3.5 - 3 = 0.5$
$\implies s - a = 1.5 , s - b = 1.5 \mathmr{and} s - c = 0.5$

$\implies A r e a = \sqrt{3.5 \cdot 1.5 \cdot 1.5 \cdot 0.5} = \sqrt{3.9375} = 1.9843$ square units

$\implies A r e a = 1.9843$ square units

Jan 22, 2016

Area = 1.98 square units

#### Explanation:

First we would find S which is the sum of the 3 sides divided by 2.

$S = \frac{2 + 2 + 3}{2}$ = $\frac{7}{2}$ = 3.5

Then use Heron's Equation to calculate the area.

$A r e a = \sqrt{S \left(S - A\right) \left(S - B\right) \left(S - C\right)}$

$A r e a = \sqrt{3.5 \left(3.5 - 2\right) \left(3.5 - 2\right) \left(3.5 - 3\right)}$

$A r e a = \sqrt{3.5 \left(1.5\right) \left(1.5\right) \left(0.5\right)}$

$A r e a = \sqrt{3.9375}$

$A r e a = 1.98 u n i t {s}^{2}$