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How to Find the Area of an Equilateral Triangle

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  • 0:04 Steps to Solve
  • 0:45 Finding the Area
  • 1:18 Another Example
  • 2:01 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Learn how you can easily find the area of an equilateral triangle. Find out what number you need to be given before you start to solve it as well as the formula to use to plug in that number.

Steps to Solve

To find the area of an equilateral triangle, or a triangle with 3 equal sides, all you have to do is to follow these steps.

Step 1

Use this formula for the area of an equilateral triangle:


Area Formula
equilateral area formula


In this case, the upper case A is the area and the lower case a is the length of the sides, which again, are all equal, hence the same letter being used.

Step 2

Plug in your value for the length of a side of your equilateral triangle and evaluate.

That is it! With a simple formula like this, calculating the area is really easy. Just plug in to the formula and evaluate!

Let's see this in action.

Finding the Area

Find the area of this equilateral triangle.


Problem
equilateral triangle


Step 1

The first step is to remember the formula, which is the square root of 3 divided by 4 multiplied by the square of the side of the equilateral triangle.


Area Formula
equilateral area formula


Step 2

The next step is to plug in the value for the side of the equilateral triangle. For this triangle, the side is 3 inches long. So, you plug in 3 for the variable s. Square that and you get 9. Multiplying the 9 by the square root of 3 and dividing by 4, you get 3.9 inches squared. And you are done!

Another Example

Let's try another one.

Find the area of an equilateral triangle with sides that measure 6 centimeters.

Step 1

First, write down the formula. The square root of 3 divided by 4 multiplied by the square of the side of the equilateral triangle.

Step 2

Your side measures 6 centimeters, so you plug in 6 to the formula. 6 squared is 36. Multiplying that by the square root of 3 and dividing by 4, you get 15.6 centimeters squared. And you are done.

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