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.
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.
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- To determine if a shape can tile the plane, check if its angles and sides allow for perfect tiling without gaps or overlaps.
Updated On: Aug 30, 2025
- circle
- regular octagon
- regular pentagon
- rhombus
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The Correct Option is A
Solution and Explanation
To tile a plane completely, the shape must have a property that allows it to cover the entire plane without gaps or overlaps.
- A circle cannot tile a plane, as it cannot fill the entire area without leaving gaps.
- A regular octagon cannot tile a plane because the angles do not fit together to fill the entire space.
- A regular pentagon also cannot tile the plane because its angles do not allow for a perfect tiling.
- A rhombus, however, can tile the plane perfectly. A rhombus can cover a flat plane by repeating and filling the entire space.
Thus, the shapes that can tile the plane are the circle and the rhombus. Final Answer: The answer is \( \boxed{\text{A}, \text{D}} \).
- A circle cannot tile a plane, as it cannot fill the entire area without leaving gaps.
- A regular octagon cannot tile a plane because the angles do not fit together to fill the entire space.
- A regular pentagon also cannot tile the plane because its angles do not allow for a perfect tiling.
- A rhombus, however, can tile the plane perfectly. A rhombus can cover a flat plane by repeating and filling the entire space.
Thus, the shapes that can tile the plane are the circle and the rhombus. Final Answer: The answer is \( \boxed{\text{A}, \text{D}} \).
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