Question

Which of the following shapes can be used to tile (completely cover by repeating) a flat plane infinitely in all directions, without leaving gaps or overlaps?

• A. Circle
• B. Regular octagon
• C. Regular pentagon
• D. Rhombus

Hint:

All parallelograms (squares, rectangles, rhombi) can tessellate. Among regular polygons, only equilateral triangles, squares, and hexagons tile perfectly.

Answer 1

The Correct Option is D

Step 1: Recall tiling rules.
To tile the plane perfectly, the shape's interior angles at a vertex must exactly sum to \(360^\circ\) when copies meet.

Step 2: Eliminate options.
- (A) Circle → cannot tile the plane, leaves gaps.
- (B) Regular octagon → does not tile by itself; needs squares to fill gaps.
- (C) Regular pentagon → cannot tile due to its \(108^\circ\) angle; multiples do not fit \(360^\circ\).

Step 3: Valid option.
(D) Rhombus → a parallelogram, and parallelograms always tessellate by repetition.

Final Answer:
\[ \boxed{\text{Rhombus}} \]