Chapter 11.5, Problem 22PPS

To determine

To find: whether the tessellation is possible or not with the given regular polygon.

Answer to Problem 22PPS

The regular $20-\text{gon}$ tessellation is not possible.

Explanation of Solution

Given information:

Consider regular $20-\text{gon}$

Concept used:

Regular tessellation is a pattern made by repeating a regular polygon.

Regular polygon has all equal sides and equal interior angles.

Calculation:

The regular $20-\text{gon}$ has $20$ equal sides and equal interior angles.

The sum of angles in $20-\text{gon}$ is

  $\begin{array}{l}=180(n-2)\\ =180(20-2)\\ ={3240}^0\end{array}$

The measure of each angle is

  $\begin{array}{l}=\frac{3240}{20}\\ =162\end{array}$

The number of polygons can tessellate $=\frac{360}{162}=2.22$

The number of polygons is not a round figure.

Hence,

The regular $20-\text{gon}$ tessellation is not possible.