The GATE Grind

GATE 2023 CH – 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

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) rhombus

Explanation

Every parallelogram, and so a rhombus, tiles the plane. A circle leaves gaps, and regular octagons and regular pentagons cannot tile alone because their interior angles (135° and 108°) do not divide 360°.