page_title: Equilateral triangle
section_title: Using the Pythagorean theorem
hierarchical_section_title: Equilateral triangle / Derivation of area formula / Using the Pythagorean theorem
context_page_description: In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. It is also a regular polygon, so it is also referred to as a regular triangle.
context_section_description: The area of a triangle is half of one side a times the height h from that side:
  The legs of either right triangle formed by an altitude of the equilateral triangle are half of the base a, and the hypotenuse is the side a of the equilateral triangle. The height of an equilateral triangle can be found using the Pythagorean theorem
  so that
  Substituting h into the area formula (1/2)ah gives the area formula for the equilateral triangle:
caption: An equilateral triangle with a side of 2 has a height of √3 as the sine of 60° is √3/2.