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

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


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.