How Many Triangles Are in a Pentagon?

Phillipe Put/CC-BY 2.0

Three triangles can be drawn inside a regular pentagon. If the diagonals are drawn from any one vertex of the pentagon, the number of triangles formed is given by the formula n – 2, where “n” is the number of sides of the polygon.

A pentagon has five sides, with three interior triangles; 5 – 2 = 3. However, if every vertex is connected to every other vertex and the triangles formed by the intersection of the diagonals are also counted, a total of 31 triangles can be formed. Dividing a pentagon into triangles can help in calculating the area of a pentagon, especially if it is an irregular pentagon. The sum of the interior angles of a pentagon is always 540 degrees.