Chapter 11.1, Problem 33WE

a.

To determine

To calculate: $t_6$ andnumber of diagonals.

Answer to Problem 33WE

The numbers of diagonals are $9$ and $t_6=9$.

Explanation of Solution

Given information:Draw a hexagon

  

From the above figure, the numbers of diagonals are $9$ .

Hence, $t_6=9$

Verify, $t_6=9$

Given information: Numbers of sides are six.

Formula used:Numbers of diagonals $=\frac{n\left(n-3\right)}{2}$ , where n is numbers of sides.

Calculation:

  $\begin{array}{l}=\frac{6\left(6-3\right)}{2}\\ =\frac{6\times 3}{2}\\ =3\times 3\\ =9\end{array}$

Hence, $t_6=9$

b.

To determine

To calculate: $t_{10}$ andnumber of diagonals.

Answer to Problem 33WE

Number of diagonals is 35 and $t_{10}=35$ .

Explanation of Solution

Given information:Numbers of sides are 10.

Formula used:Numbers of diagonals $=\frac{n\left(n-3\right)}{2}$ , where n is numbers of sides.

Calculation:

  $\begin{array}{l}=\frac{10\left(10-3\right)}{2}\\ =\frac{10\times 7}{2}\\ =5\times 7\\ =35\end{array}$

Hence, $t_{10}=35$