# Equilateral triangle area formula explained

Learn and know the formula for area of equilateral triangle and also know the idea by which we can derive the formula. This is one of the important formulas related to areas in types of triangles.

First we need to know what is an equilateral triangle. Basically we call or we say a triangle as the equilateral triangle if it has all the three sides equal in their measurements. For this triangle we are going to learn the formula for finding the area. This formula is actually derived from the Herons Formula. So just check Herons formula so that you can get one idea to derive the formula for area of equilateral triangle. Now I will give you the direct formula without derivation. If you need derivation you can do it yourself by Herons formula.

## The formula for area of equilateral triangle as follows:

Let ΔPQR be an equilateral triangle. Assume that “n” be the side of an equilateral triangle ΔPQR, which means all the sides of an equilateral triangle are equal to “n”. Therefore, the formula for finding the area of equilateral triangle is given by $\frac { \sqrt { 3 } }{ 4 }×{ n }^{ 2 }$.

Examples:

Area of equilateral triangle whose side is 6 cm = $\frac { \sqrt { 3 } }{ 4 }× { n }^{ 2 }$ = $\frac { \sqrt { 3 } }{ 4 }× { 6 }^{ 2 }$=$\frac { \sqrt { 3 } }{ 4 }$ × 36 = $\sqrt { 3 }$ × 9 = 1.732 × 9 = 15.59 ${ cm }^{ 2 }$.

Area of equilateral triangle whose side is 2 cm = $\frac { \sqrt { 3 } }{ 4 }× { 2 }^{ 2 }$ = $\frac { \sqrt { 3 } }{ 4 }$ × 4 = $\sqrt { 3 }$ = 1.732 ${ cm }^{ 2 }$.

Area of equilateral triangle whose side is 8 cm = $\frac { \sqrt { 3 } }{ 4 } ×{ 8 }^{ 2 }$ = $\frac { \sqrt { 3 } }{ 4 }$ × 64 = $\sqrt { 3 }$ × 16 = 1.732 × 16 = 27.71 ${ cm }^{ 2 }$.

Area of equilateral triangle whose side is 10 cm = $\frac { \sqrt { 3 } }{ 4 } ×{ 10 }^{ 2 }$ = $\frac { \sqrt { 3 } }{ 4 }$ × 100 = $\sqrt { 3 }$ × 25 = 1.732 × 25 = 43.30 ${ cm }^{ 2 }$.

I Hope that the formula of area of equilateral triangle and examples are clear without any confusion.