Question

question 5 of 10

which of the following can be used to create a regular tessellation?

check all that apply.

a. square
b. regular pentagon
c. equilateral triangle
d. regular hexagon
e. rectangle

Explanation:

Define regular tessellation

Using the Regular Tessellation knowledge point
A regular tessellation is a tiling of the plane using a single type of regular polygon such that the shapes fit together at every vertex without gaps or overlaps.

Calculate interior angles

Using the Regular Tessellation knowledge point
For a regular polygon with \(n\) sides, the interior angle is:

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

• Equilateral triangle (\(n=3\)): \(\theta = 60^\circ\)
• Square (\(n=4\)): \(\theta = 90^\circ\)
• Regular pentagon (\(n=5\)): \(\theta = 108^\circ\)
• Regular hexagon (\(n=6\)): \(\theta = 120^\circ\)

Determine vertex compatibility

Using the Regular Tessellation knowledge point
For a regular polygon to tessellate, its interior angle \(\theta\) must divide \(360^\circ\) exactly:

• Triangle: \(\frac{360^\circ}{60^\circ} = 6\) (integer)
• Square: \(\frac{360^\circ}{90^\circ} = 4\) (integer)
• Pentagon: \(\frac{360^\circ}{108^\circ} \approx 3.33\) (not an integer)
• Hexagon: \(\frac{360^\circ}{120^\circ} = 3\) (integer)

Evaluate non-regular shapes

Using the Regular Tessellation knowledge point
A rectangle is not a regular polygon because its sides are not all equal, so it cannot form a regular tessellation by definition.

Answer:

• A. Square (Correct answer)
• B. Regular pentagon
• C. Equilateral triangle (Correct answer)
• D. Regular hexagon (Correct answer)
• E. Rectangle