Chapter 10.5, Problem 69E

a.

To determine

To calculate:

Expression for the number of diagonals in $n-$ sided polygon.

Answer to Problem 69E

Expression for the number of diagonals in $n-$ sided polygon is $C{}_{n-2}-n$ .

Explanation of Solution

Given information:

  

Calculation:

There is a convex polygon with $n$ sides. It is required to write an expression using combination formula for the diagonals of the polygon.

The expression for combination is given by,

  $C{}_{n-2}-n$

Where,

  $n=$ denotes number of sides.

Thus, answer is $C{}_{n-2}-n$ .

b.

To determine

To calculate:

Expression for the number of diagonals in $n-$ sided convex polygon by using result of part (a).

Answer to Problem 69E

Expression for the number of diagonals in $n-$ sided convex polygon is $\frac{n\left(n-3\right)}{2}$ .

Explanation of Solution

Given information:

  

Calculation:

There is a convex polygon with $n$ sides. It is required to write an expression using combination formula for the diagonals of the polygon.

The expression for combination is given by,

  $\frac{n\left(n-3\right)}{2}$

Where,

  $n=$ denotes number of sides of convex polygon

Thus, answer is $\frac{n\left(n-3\right)}{2}$ .