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Area Of Equilateral Triangles

Area Of Equilateral Triangles

Author: c o

The student will learn how to derive the formula for finding the area of equilateral triangles.

In this lesson background material is briefly covered before the formula is introduced and then derived in a video.

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Before starting this lesson you should already be familiar witht he following.

Equilateral Triangle

An equilateral triangle is just a triangle for which all three sides are of equal length.  E.g.

Area of a Triangle

Given a triangle's base and height, finding the area of the triangle should be a familar calculation.

Pythagorean Theorem

Given a right triangle, you should be familiar with the relationship between its sides and its hypotenuse.

For review, check out this lesson on the pythagorean theorem.

Special Triangles

Some familiarity with special triangles will also be helpful but not necessary.  See here or here for background.

Area of an Equilateral

The Formula

Given an equilateral triangle with side length s, the formula for the area of that triangle is

For Example

If this is our triangle

then s = 4 so that the area is

(√3 X 42)/4 = 

√3 X 4 =


Derivation of the Formula

Using the Pythagorean formula and the standard triangle area formula, the formula for the area of an equilateral triangle is derived.

Source:, Colin O'Keefe