Question

question 4 of 10

its possible to create a regular tessellation with a regular heptagon.

a. true

b. false

Explanation:

Calculate the interior angle of a regular heptagon

Using the Regular Tessellation and Tessellation Definition knowledge points

$$ \theta = \frac{(n-2) \times 180^\circ}{n} = \frac{(7-2) \times 180^\circ}{7} = \frac{900^\circ}{7} \approx 128.57^\circ $$

Check the vertex divisibility condition

Using the Regular Tessellation knowledge point

$$ \frac{360^\circ}{\theta} = \frac{360^\circ}{\frac{900^\circ}{7}} = \frac{360 \times 7}{900} = \frac{14}{5} = 2.8 $$

Since \(2.8\) is not an integer, a regular heptagon cannot tile a flat plane without gaps or overlaps.

Answer:

• A. True
• B. False (Correct answer)