# Area of Equilateral Triangle

Sub Topics
The triangle is a polygon with the least number of sides. This fact that the triangle encloses a well defined plane region made it possible to find the perimeter enclosing and the area enclosed using formulas.

Measurement problems on plane figures mainly involve perimeter and area. The two formulas for a general scalene triangle are

Perimeter of a triangle = a + b + c
where a, b and c are the lengths of the sides of the triangle.

Area of a triangle = $\frac{1}{2}$.bh
Where 'b' the base is the length of a side and 'h' the corresponding height.

## Area of Equilateral Triangle Formula

Now substituting this value of h in the formula for the area of the triangle

2s = a + b + c

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

Area of a triangle =$\frac{1}{2}$.bh

Area of an equilateral triangle of side ‘a’ = $\frac{\sqrt{3a^2}}{4}$

## How to Find the Area of an Equilateral Triangle

Below you could see how to find the area of an equilateral triangle

## Perimeter of an Equilateral Triangle

An equilateral triangle is a triangle with three congruent sides. This attribute simplifies the formulas for perimeter and area further.

Since the three sides are of equal lengths in an equilateral triangle, a = b = c.
Perimeter of equilateral triangle = 3a

Where a is the length of the side.

## Height of Equilateral Triangle

The equiangular property of an equilateral triangle enables the h to be written in terms of the base.
 In the equilateral triangle each side is of length a units, and each angle measures 60o. CD is the altitude drawn to side ABApplying Pythagorean theorem for the right triangle ADC, h2+$(\frac{a}{2})^2$=a2→h2+$\frac{a^2}{4}$=a2 h2+$\frac{3a^2}{4}$→h = $\frac{\sqrt{3}}{2}$ Height of an equilateral triangle of side 'a' = $\frac{\sqrt{3a}}{2}$