How many diagonals can be drawn by joining the vertices of an octagon

Geometry

How many diagonals can be drawn by joining the vertices of an octagon?

  1. 20
  2. 24
  3. 28
  4. 64

Answer

If you draw an octagon (eight-sided polygon), select one vertex and construct each diagonal from this vertex, you will see there are 5 such diagonals. Thus, for each of the 8 vertices you can draw 5 diagonals and hence there can be 5 × 8 = 40 diagonals. But, each diagonal is counted twice, once from each of its ends. Thus, there are 20 diagonals in a regular octagon.

Using the formula, to draw a diagonal, you have to select two vertices out of n, but you cannot draw diagonal by joining the adjacent vertex.

Number of diagonals = nC2 – n , where n is the number of sides of the polygon.

For octagon, n = 8. Hence,

Number of diagonals = 8C2 - 8 = 28 - 8 = 20.

The correct option is A.