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GATE 2022 ME (ME2) – Question 5

General Aptitude · Spatial Aptitude: Spatial Reasoning and Visualization · 1 mark · Multiple choice

Which one of the groups given below can be assembled to get the shape that is shown above using each piece only once without overlapping with each other? (rotation and translation operations may be used).

a narrow pointed shape with a flared base; four alternative groups of polygonal pieces.
  1. Option A in the figure
  2. Option B in the figure
  3. Option C in the figure
  4. Option D in the figure

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Show answer and explanation

Correct answer: (B) Option B in the figure

Explanation

The target shape has a narrow pointed top, a long stem and a flared base, so the pieces have to be sorted by what part of the shape they can fill.

1. **Stem:** the long, uniform vertical part is a rectangle.
2. **Pointed cap:** one triangle forms the top.
3. **Flared base:** the base widens like a trapezoid. A trapezoid can be tiled by **three equal triangles** (two pointing one way and one the other way).

So the group must contain **one rectangle and four triangles** (one for the cap and three for the base). Of the four groups shown, only B has exactly these pieces, and the pieces can be rotated and translated to fit without overlap.