# Area of an equilateral triangle

The area of an equilateral triangle can be found by using the Pythagorean formula: 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 so you can master geometry. ## Recent Articles 1. ### Introduction to Physics

Nov 18, 20 01:20 PM

Top-notch introduction to physics. One stop resource to a deep understanding of important concepts in physics

New math lessons

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

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius! Real Life Math Skills

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