Chapter 14.8, Problem 20WE

a.

To determine

To write whether the tessellation can be made with a regular hexagon.

Answer to Problem 20WE

Since angles of a hexagon are $120°$ therefore they can form a tessellation because when 3 regular hexagon meet each other at point and completes $360°$

Explanation of Solution

Given information:

The given statement is that whether the tessellation can be made with a regular hexagon.

Measure of each angle of a regular hexagon.

  $\begin{array}{l}m\angle =\left(n-2\right)\times \frac{180°}{n}\\ =\left(6-2\right)\times \frac{180°}{6}\\ =120°\end{array}$

Since angles of a hexagon are $120°$ therefore they can form a tessellation because when 3 regular hexagon meet each other at point and completes $360°$ as shown in below figure.

  

b.

To determine

To write whether the tessellation can be made with a scalene triangle.

Answer to Problem 20WE

It is possible to form tessellation with scalene triangle but not in each case, it is possible if the angles of the scalene triangle are product of $360°$

Explanation of Solution

Given information:

The given statement is that whether the tessellation can be made with a scalene triangle.

It is possible to form tessellation with scalene triangle but not in each case, it is possible if the angles of the scalene triangle are factor of $360°$

c.

To determine

To write whether the tessellation can be made with a regular pentagon.

Answer to Problem 20WE

Since angles of a hexagon are $120°$ therefore they can form a tessellation because when 3 regular hexagon meet each other at point and completes $360°$ .

Explanation of Solution

Given information:

The given statement is that whether the tessellation can be made with a regular hexagon.

Measure of each angle of a regular polygon.

  $\begin{array}{l}m\angle =\left(n-2\right)\times \frac{180°}{n}\\ =\left(5-2\right)\times \frac{180°}{5}\\ =108°\end{array}$

Since angles of a hexagon are $108°$ therefore they cannot form a tessellation because $108°$ is not a factor of $360°$ .

d.

To determine

To write whether the tessellation can be made with a non-isosceles trapezoid.

Answer to Problem 20WE

It is possible to form tessellation with scalene triangle but not in each case, it is possible if the angles of the scalene triangle are product of $360°$

Explanation of Solution

Given information:

The given statement is that whether the tessellation can be made with a non-isosceles trapezoid.

It is possible to form tessellation with non-isosceles trapezoidbut not in each case, it is possible if the angles of the scalene triangle are factor of $360°$