Chapter 8.5, Problem 74E

To determine

To find: the number of diagonals of the polygon.

Answer to Problem 74E

The number of diagonals of the Hexagon is 9.

Explanation of Solution

Given Information:

Hexagon

Concept used:

A line segment connection any two nonadjacent vertices is called a diagonal of a polygon.

Calculation:

The number of combinations of $n$ elements taken $r$ at a time is

  ${}_n{C}_r=\frac{n!}{\left(n-r\right)!r!}$

Here,

  $\begin{array}{l}n=6\\ n=2\end{array}$

The number of diagonal of the Hexagon can be calculated as

  $\begin{array}{c}{}_6{C}_2-6=\frac{6!}{2!\left(6-2\right)!}-6\\ =\frac{6\times 5\times 4!}{2\times 1\times 4!}-6\\ =15-6\\ =9\end{array}$

Hence, the number of diagonals of the Hexagon is 9.