Area of an equilateral triangle

The area of an equilateral triangle can be found by using the Pythagorean formula:

Start with any equilateral triangle

Equilateral triangle

Label the sides.
Equilateral triangle

Draw the perpendicular bisector of the equilateral triangle as shown below. Note how the perpendicular bisector breaks down side a into its half or a/2

Area of an equilateral triangle

Now apply the Pythagorean theorem to get the height (h) or the length of the line you see in red

a2 = (a/2)2 + h2

a2 = a2/4 + h2

a2 − a2/4 = h2

4a2/4 − a2/4 = h2

3a2/4 = h2

h = √(3a2/4)

h = (√(3)×a)/2

Area = (base × h)/2

base × h = (a × √(3)×a)/2 = (a2× √(3))/2

Dividing by 2 is the same as multiplying the denominator by 2. Therefore, the formula is

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