Chapter 8.2, Problem 42PPE

a.

To determine

To find: Number of sides of the polygon and diagonal that comes from one vertex

Answer to Problem 42PPE

Number of sides of the polygon is 6 and diagonal coming from one vertex is 3

Explanation of Solution

Given:

  

Calculation:

By the diagram, we can say that the number of sides of the polygon is 6 and the diagonals comes from one vertex is 3

b.

To determine

To find: The number of diagonals that the polygon that has n sides will have.

Answer to Problem 42PPE

  $n-3$

Explanation of Solution

Given:

The polygon has n sides

Calculation:

The number of diagonals from a vertex of polygon that have n sides is n − 3

c.

To determine

To write: The polynomial in standard form

Answer to Problem 42PPE

  $0.5n^2-1.5n$

Explanation of Solution

Given:

The number of diagonals from all the vertices is $\frac{n}{2}\left(n-3\right)$

Calculation:

The standard form is:

  $\begin{array}{l}\frac{n}{2}\left(n-3\right)=0.5n\left(n-3\right)\\ \frac{n}{2}\left(n-3\right)=0.5n^2-1.5n\end{array}$

d.

To determine

To find: The number of diagonals of polygon

Answer to Problem 42PPE

Number of diagonals is 5

Explanation of Solution

Given:

A polygon has 8 sides

Calculation:

The formula for number of diagonals when number of sides of the polygon given is:

  $n-3$

Apply the formula:

  $\begin{array}{l}8-3\\ 5\end{array}$