Geometry Practice : Properties of Polygons

This quant practice question is a geometry problem solving question. Concept tested: Number of triangles in a polygon.

Question

Find the number of triangles in an octagon.

1. 326
2. 120
3. 56
4. Cannot be determined

  Correct Answer      Choice (3). An octagon has 56 triangles

Explanatory Answer

No three vertices of a polygon will line on a straight line. Therefore, joining any 3 vertices of a polygon will result in a triangle.
An n-sided polygon will have n vertices.
Number of triangles that can be formed = number of ways of selecting 3 vertices out of n vertices = ⁿC₃.

An octagon has 8 sides and 8 vertices.
In this question n = 8 => number of triangles =⁸C₃ = 56.

  The correct answer is Choice (3).