An equilateral triangle is a triangle in which all three sides have the same length. As a consequence, all interior angles are the same ().
EquilateralTriangleLabelled.png
Consider an equilateral triangle with side length and let represent its height. The area is then . More generally, if an equilateral triangle has base length then its height is and so its area is .
Cutting the triangle in half from a vertex to the midpoint of the opposite side results in two triangles that can be put back together to form an isosceles triangle with angles , , and . The base of this triangle is twice the height of the original, so is .
EquilateralTriangleDissected.png
Three of these triangles fit together to form a new equilateral triangle. As this new triangle has base its area is . It also is three copies of the original triangle so its area is . Putting these together, and so .
The height and area of an equilateral triangle of base length are therefore respectively
and of base length