Question

question 3 of 10
which of the following can be used to create a regular tessellation?
check all that apply.
a. equilateral triangle
b. regular octagon
c. square
d. regular hexagon
e. regular heptagon

Explanation:

Step1: Formula for interior angle of a regular polygon

The formula for the interior angle of a regular polygon is $\theta=\frac{(n - 2)\times180^{\circ}}{n}$, where $n$ is the number of sides of the polygon.

Step2: Calculate interior angles

• For an equilateral triangle ($n = 3$): $\theta=\frac{(3 - 2)\times180^{\circ}}{3}=60^{\circ}$. And $360\div60 = 6$, so equilateral triangles can tessellate.
• For a square ($n = 4$): $\theta=\frac{(4 - 2)\times180^{\circ}}{4}=90^{\circ}$. And $360\div90=4$, so squares can tessellate.
• For a regular hexagon ($n = 6$): $\theta=\frac{(6 - 2)\times180^{\circ}}{6}=120^{\circ}$. And $360\div120 = 3$, so regular hexagons can tessellate.
• For a regular octagon ($n = 8$): $\theta=\frac{(8 - 2)\times180^{\circ}}{8}=135^{\circ}$. And $360\div135=\frac{8}{3}

otin\mathbb{Z}$, so regular octagons cannot tessellate.

• For a regular heptagon ($n = 7$): $\theta=\frac{(7 - 2)\times180^{\circ}}{7}\approx128.57^{\circ}$. And $360\div\frac{(7 - 2)\times180^{\circ}}{7}=\frac{14}{5}

otin\mathbb{Z}$, so regular heptagons cannot tessellate.

Answer:

A. Equilateral triangle, C. Square, D. Regular hexagon