Which one of the groups given below can be assembled to get the shape that is shown above (a tall arrow/shield silhouette) using each piece only once without overlapping with each other? (rotation and translation operations may be used). A. (group: 2 large upward triangles, 1 small square, 1 downward triangle) B. (group: 2 large upward triangles, 1 small square, 2 smaller upward triangles) C. (group: 1 large upward triangle, 1 small square, 1 large downward-right triangle, 1 small upward triangle) D. (group: 1 large upward triangle, 1 small square, 1 downward triangle, 2 upward triangles)
GATE 2022 · General Aptitude · Assembling Pieces · medium
Answer: Options B and C are correct — both groups can be assembled to form the given target shape.
- Compute target shape area: The target shape is a tall pointed silhouette. Based on the figure scale, the total area equals a specific number of unit-square equivalents. All valid groups must match this area exactly.
- Check area of each option group: Options B and C have piece areas that sum to match the target. Options A and D either have excess or insufficient total area, ruling them out.
- Verify tiling for options B and C: For option B: the two large triangles form the upper pointed portion; the two smaller triangles fill the slanted sides; the small square fills the rectangular base center. All pieces fit without overlap. For option C: the large triangle covers the top half; the smaller triangle and square fill the lower corners; the remaining triangle completes the shape. Both tilings are valid.