# Area of an Equilateral Triangle Calculator

**Area of an equilateral triangle -**An equilateral triangle has all its sides as equal. The perpendicular drawn from the vertex of the triangle to the base divides the base into two equal parts. To calculate the area of the equilateral triangle, we have to know the measurement of its sides.

### What is meant by Area of an Equilateral Triangle?

The area of an equilateral triangle is defined as the amount of space that remains on a 2D closed surface. Firstly, remember that an equilateral triangle is a triangle where all of its sides are equal and the measurement of all the internal angle is 60º. All the angles in an equilateral triangle are congruent. As triangle is a 2D figure it has both area and perimeter.

Thus, finding an equilateral triangle area is very easy if you have the length of its side. Apply the side value in the formula of area of an equilateral triangle and get the area for the Math problems.

### Formula of Area of an Equilateral Triangle

The formula for the area of an equilateral triangle is given as:

**Area of Equilateral Triangle (A) = (√3/4)s2 or (√3/4)a2 **

Where s and a represent length of sides.

### Derivation of Area of an Equilateral Triangle

First, take an equilateral triangle of the side as 'a' unit. Then all sides of a triangle are '3a' now draw a perpendicular bisector to the base of height 'h'.

Now take the Area of Triangle formula i.e., Area = ½ × base × height

Here, we are assuming base = a, and height = h

Now, apply Pythagoras Theorem in the triangle.

a2 = h2 + (a/2)2

⇒ h2=a2–a2/4

⇒ h2=(3a2)/4 Or h=½(√3a)

Now, put the value of 'h' in the area of the triangle equation.

So, Area of Triangle = ½ × base × height

⇒ A = ½ × a × ½(√3a)

Thus, **Area of Equilateral Triangle = ¼(√3a2) or (√3/4)a2**

### How to Calculate the Area of an Equilateral Triangle?

If you know the side of an equilateral triangle, then apply the input in the formula of area of an equilateral triangle

ie., Area of an Equilateral Triangle (A) = (√3/4)a2

Where 'a' is the length of any side of the triangle

**OR**

Note that √3/4 is constant that has a value of approximately 0.433, so the formula of an Area of an Equilateral Triangle is A = 0.433a2. (approximately).

**Solved Example**

**Question 1:** What is the area of an equilateral triangle whose side is 3.7 cm?

**Solution:**

Given that side = 3.7 cm

**Area of an Equilateral Triangle (A) = (√3)/4 × a2**

Put the value of side in Area Formula.

Area= (√3)/4 × 3.72

⇒ Area = (√3)/4 x 3.7 x 3.7

Multiply 3.7 cm and 3.7 cm

⇒ Area = (√3)/4 x 13.69

⇒ Area = 1.732/4 x 13.69

⇒ Area = 0.433 x 13.69

⇒ Area= 5.92777 cm2

Therefore, Area of an Equilateral Triangle side 3.7 cm is **5.92777 cm2**

### Steps to Use our online Area of an Equilateral Triangle Calculator

Go through these below easy steps on how to use the calculator to find the area of an equilateral triangle. By using our handy Equilateral Triangle Area Calculator, you can make your calculations extremely easier and faster. So, follow these simple steps and find the area of an equilateral triangle for any type of unit you required.

- Enter the Equilateral Triangle Side in the input field
- After that, choose the required Unit metric for a triangle side as cm,m, ft, yd, mi, etc. from the dropdown list.
- Later click on the 'Area' button which is located below to the input box.
- Finally, you will get the output on the screen along with a detailed explanation.