Area of Equilateral Triangle

Activity

Take a paper and make an equilateral triangle. Fold it from any vertex to the opposite base side to bisect it. Observe the relationship between the altitude and the base.

Derivation

Let the side of the equilateral triangle be a. Draw perpendicular AD on BC.
BD = DC =
a2


By Pythagoras Theorem:
AD = √(AC² - CD²) = √(a² - (a/2)²) =
√32
a

Area = ½ × base × height = ½ × a ×
√32
a

Area (A) =
√34
a²