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  • The number of diagonals that can be drawn by connecting an octagon's vertices isOption: 1 20Option:

The number of diagonals that can be drawn by connecting an octagon's vertices is

Option: 1

20


Option: 2

18


Option: 3

12


Option: 4

22


Answers (1)

best_answer

It is known that an octagon has eight sides.

As a result, it contains 8 vertices.

Thus, we must determine the number of lines that can be drawn from eight 8 points.

We know that a line is drawn with the help of two points.

To draw a line, we must select two points from a set of eight.

Therefore,

The number of lines that can be drawn from 8 points is given by,

\begin{aligned} &{ }^8 C_2=\frac{8 !}{2 ! 6 !}\\ &{ }^8 C_2=\frac{8 \times 7}{2}\\ &{ }^8 C_2=28 \end{aligned}

As a result, 28 lines with 8 points can be drawn.

The octagon has 8 lines as sides,

To get the number of diagonals, subtract 8 from the total number of lines.

The number of diagonals is given by,

N = Total number of lines - Total number of sides of an octagon

N = 28 - 8

N = 20

Therefore, the total number of diagonals formed is 20.

Posted by

rishi.raj

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