Question

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

20
24
28
64

Answer 1

Answer:

The correct option is A.

Explanation:

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.

Answer 2

$\huge\red{\boxed{\bold{Answer}}}$

20 Diagonals.

$\huge\underline\mathfrak\green{Explanation}:$

Thus for each of the 8 vertices you can draw 5 diagonals and hence you have constructed 5 × 8 = 40 diagonals.

But you have constructed each diagonal twice, once from each of its ends.

Thus there are 20 diagonals in a regular octagon.

$\huge\mathbb\blue{THANK\:YUH!}$