Chapter 11.5, Problem 21PPS

To determine

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

Answer to Problem 21PPS

The $15-\text{gon}$ tessellation is not possible.

Explanation of Solution

Given information:

Consider regular $15-\text{gon}$

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 $15-\text{gon}$ has $15$ equal sides and equal interior angles.

The sum of angles in $15-\text{gon}$ is

  $\begin{array}{l}=180(n-2)\\ =180(15-2)\\ ={2340}^0\end{array}$

The measure of each angle is

  $\begin{array}{l}=\frac{2340}{15}\\ =156\end{array}$

The number of polygons can tessellate $=\frac{360}{156}=2.30$

The number of polygons is not a round figure.

Hence,

The $15-\text{gon}$ tessellation is not possible.