# Area of an Equilateral Triangle

An equilateral triangle has three equal sides and angles. As in any type of triangle, its area is equal to half of the product of its base and height. So if the altitude of an equilateral triangle is:

The **area of an Equilateral Triangle** it will be defined by the following formula:

## How do you find the area of an equilateral triangle?

The area of an **equilateral triangle** is obtained as the base product (side *a*) by the height (*h*) divided by two (*Note*: *why is the area of a triangle a half of the base product by height?*).

Let’s see what the **height of the equilateral triangle**.

This can be calculated from Pythagorean theorem. The sides *a*, *a/2* and *h* form a right triangle. The sides *a/2* and *h* are the legs and *a* the hypotenuse.

Applying the Pythagorean theorem:

Another procedure to calculate its **altitude** would be from trigonometric ratios.

With respect to the 60º angle, the ratio between the height *h* and the hypotenuse of triangle *a* is equal to sine of 60º. Therefore:

We obtain that the **height** (*h*) of equilateral triangle is:

Now, applying that **area** is a half of the product of **base** (*a*) by **height** (*h*):

And we arrive at the formula of the area of equilateral triangle is:

Download this **calculator** to get the results of the formulas on this page. Choose the initial data and enter it in the upper left box. For results, press ENTER.

Triangle-total.rar or Triangle-total.exe

Note. Courtesy of the author: **José María Pareja Marcano**. Chemist. Seville, Spain.

## Exercise

Find the **area** of an **equilateral triangle** in which its three equal sides have the length *a*=5 cm.

What is its **area**?

Applying the above formula:

The area is **10.83 cm ^{2}**.

## Table of Triangle Area Formulas

You can see the **table of triangle area formulas **. Depending on the type of triangle you may need one element ( equilateral triangle), two (base and height) or three (as long as they are not the three angles).