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

- 20
- 24
- 28
- 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 = ^{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.**

- PQ is parallel to RS and PR is parallel to QS, If ∠LPR = 35°
- ABC is an isosceles triangle such that AB = BC = 8 cm
- PQRS is a parallelogram. PA bisects angle P and SA bisects angle S
- Consider obtuse angled triangles with sides 8 cm, 15 cm and x cm
- What is the length of the perpendicular drawn from the centre