# Number of Triangles Contained in a Polygon

We will learn how to find the number of triangles contained in a polygon.

If the polygon has ‘n’ sides, then the number of triangle in a polygon is (n – 2).

 In a triangle there are three sides. In the adjoining figure of a triangle ABC we can observe that the number of triangles contained = 3 – 2 = 1. In a quadrilateral there are four sides. Number of triangles contained in a quadrilateral = 4 – 2 = 2. In the adjoining figure of a quadrilateral ABCD, if diagonal BD is drawn, the quadrilateral will be divided into two triangles i.e. ∆ABD and ∆BDC. In a pentagon there are five sides. Number of triangles contained in a pentagon = 5 – 2 = 3. In the adjoining figure of a pentagon ABCDE, on joining AC and AD, the given pentagon is divided into three triangles i.e. ∆ABC, ∆ACD and ∆ADE. In a hexagon there are six sides. Number of triangles contained in a hexagon = 6 – 2 = 4. In the adjoining figure of a hexagon ABCDEF, on joining AC, AD and AE, the given hexagon is divided into four triangles i.e. ∆ABC, ∆ACD, ∆ADE and ∆AEF. Polygons

Polygon and its Classification

Terms Related to Polygons

Interior and Exterior of the Polygon

Convex and Concave Polygons

Regular and Irregular Polygon

Number of Triangles Contained in a Polygon

Angle Sum Property of a Polygon

Sum of the Exterior Angles of a Polygon