# 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?

- 20
- 24
- 28
- 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 = ^{n}C_{2} – n , where n is the number of sides of the polygon.

For octagon, n = 8. Hence,

Number of diagonals = ^{8}C_{2} - 8 = 28 - 8 = 20.

**The correct option is A.**