Area of an equilateral triangle


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



Start with any equilateral triangle




Label the sides.


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



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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