It's possible to create a regular tessellation with a regular pentagon.A.TrueB.FalseSUBMITarrow_backPREVIOUS

Break Down the Problem

1. Evaluate the properties of regular tessellations.
2. Understand the characteristics of regular polygons and their angles.

Relevant Concepts

1. A regular tessellation is formed when a single shape completely covers a plane without gaps or overlaps, and this shape must be a regular polygon.
2. The interior angle of a regular pentagon is given by the formula: $\text{Interior Angle} = \frac{(n-2) \cdot 180^\circ}{n}$ where $n$ is the number of sides.

Analysis and Detail

1. For a regular pentagon ($n = 5$): $\text{Interior Angle} = \frac{(5-2) \cdot 180^\circ}{5} = \frac{3 \cdot 180^\circ}{5} = 108^\circ$
2. To determine if a shape can tessellate, the interior angles must fit evenly around a point (i.e., they must sum to $360^\circ$).
   • $\frac{360^\circ}{108^\circ} \approx 3.33$, which is not an integer.

Verify and Summarize

Since the interior angles of the pentagon do not neatly sum to $360^\circ$ around a vertex, a regular pentagon cannot create a regular tessellation.

Final Answer

B. False