Chapter 11.5, Problem 6CYU

To determine

To find: whether the tessellation is possible using only with equilateral triangles or not.

Answer to Problem 6CYU

The tessellation is possible using equilateral triangles, squares and regular hexagons.

Explanation of Solution

Given information:

Consider tessellation.

Concept used:

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

Regular polygon has all equal sides and equal interior angles.

Calculation:

Consider square,

The measure of each angle in square is $={90}^0$

The number of squares can tessellate $=\frac{360}{90}=4$

Consider regular hexagon,

The measure of each angle in regular hexagon is $={120}^0$

The number of regular hexagons can tessellate $=\frac{360}{120}=3$

The tessellation is possible using equilateral triangles, squares and regular hexagons.