Question

Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and are not allowed to overlap.

• A. circle
• B. regular octagon
• C. regular pentagon
• D. rhombus

Hint:

Shapes that can tile a plane must be able to fill the entire area without gaps or overlaps. Circles and rhombuses are examples of such shapes.

Answer 1

The Correct Option is A

- Circles (A): The tiling of a plane with identical circles is possible because circles can be placed adjacent to each other without leaving any gaps. This is the most common way to tile a plane using circles.
- Rhombus (D): A rhombus, being a parallelogram, can also tile the plane completely without gaps. The rhombus shape allows perfect tiling with no overlap and no gaps between tiles.
- Regular octagon (B) and regular pentagon (C): These shapes cannot tile the plane completely without gaps or overlaps, hence they are not suitable for tiling in this context.
- Therefore, the correct answers are circles (A) and rhombus (D).