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


Buy a comprehensive geometric formulas ebook. All geometric formulas are explained with well selected word problems.

Recent Articles

  1. Probability Line - Definition and Examples

    Nov 21, 19 02:38 PM

    What is a probability line ? Things that you must know before doing problems ...

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

                                 Follow me on Pinterest

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.