Question

question 21 of 40
a hexagon forms a semi-regular tessellation with which of the following regular polygons?
a. square and equilateral triangle
b. trapezoid and pentagon
c. dodecagon and equilateral triangle
d. trapezoid and octagon

Explanation:

A semi-regular tessellation requires the sum of interior angles at each vertex to equal 360°, using regular polygons. First, calculate the interior angle of a regular hexagon: $\frac{(6-2)\times180^\circ}{6}=120^\circ$.

• For option A: Interior angle of square is $90^\circ$, equilateral triangle is $60^\circ$. A valid combination is $120^\circ + 120^\circ + 60^\circ + 60^\circ = 360^\circ$, which forms a known semi-regular tessellation.
• Options B, D include trapezoid, which is not a regular polygon, so they are invalid.
• Option C: Interior angle of dodecagon is $150^\circ$, triangle is $60^\circ$. No combination of these with $120^\circ$ sums to $360^\circ$.

Answer:

A. Square and equilateral triangle