Number of Triangles Contained in a Polygon

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.