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GATE 2023 MT – Question 10

General Aptitude · Spatial Aptitude: Spatial Reasoning and Visualization · 2 marks · Multiple choice

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.

  1. circle
  2. regular octagon
  3. regular pentagon
  4. rhombus

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Show answer and explanation

Correct answer: (D) rhombus

Explanation

Every parallelogram tiles by translations along its two side vectors; a rhombus is a parallelogram. Regular pentagons and octagons leave angular gaps when used alone, and congruent circles cannot cover without gaps or overlaps.

Thus **rhombus, D**.