# Area of an Equilateral Triangle

#### Find the area of an equilateral triangle of side a.

SOLUTION:

Using Heron’s Formula, the formula of the triangle is given by

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

where s is the semi-perimeter, $s=\frac{a+b+c}{2}$

Since it is an equilateral triangle, a=b=c.

$s=\frac{a+a+a}{2}=\frac{3a}{2}$

Threfore, the area is

$A=\sqrt{\frac{3a}{2}\left(\frac{3a}{2}-a\right)^3}$

$A=\sqrt{\frac{3a}{2}\left(\frac{a}{2}\right)^3}$

$A=\sqrt{\frac{3a}{2}\left(\frac{a^3}{8}\right)}$

$A=\sqrt{\frac{3a^4}{16}}$

$A=\frac{\sqrt{3}}{4}a^2$

Do you have difficulties in your studies? The engineering-math.org is here to help you. You can now book for an online live tutoring here

We also cater help in any online course. Just email us at enggmathem@gmail.com.