Chapter 11.5, Problem 20PPS

To determine

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

Answer to Problem 20PPS

The $12-\text{gon}$ tessellation is not possible.

Explanation of Solution

Given information:

Consider regular $12-\text{gon}$

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 $12-\text{gon}$ has $12$ equal sides and equal interior angles.

The sum of angles in $12-\text{gon}$ is

  $\begin{array}{l}=180(n-2)\\ =180(12-2)\\ ={1800}^0\end{array}$

The measure of each angle is

  $\begin{array}{l}=\frac{1800}{12}\\ =150\end{array}$

The number of polygons can tessellate $=\frac{360}{150}=2.4$

The number of polygons is not a round figure.

Hence,

The $12-\text{gon}$ tessellation is not possible.