A black square PQRS has been cut into two parts. One part of it is shown in
Panel I. Which one of the shapes in Panel II is the other part?
A black square PQRS has been cut into two parts. One part of it is shown in
Panel I. Which one of the shapes in Panel II is the other part?
Show Hint
- (i)
- (ii)
- (iii)
- (iv)
The Correct Option is C
Solution and Explanation
Step 2: For a shape in Panel II to be the correct missing piece, two conditions must hold: (a) its area must exactly equal the area of the square minus the area of the piece shown in Panel I, and (b) the boundary edge created by the cut on it must be the exact complementary mirror image of the cut edge on the Panel I piece, so the two pieces interlock perfectly to reform a full square with no gaps or overlaps.
Step 3: Checking each shape in Panel II against the piece in Panel I, only shape (iii) has a cut boundary that is the precise complement of the boundary in Panel I - every notch that points inward on one piece points outward by the same amount on the matching piece, and the combined area equals the area of square PQRS.
Step 4: Shapes (i), (ii), and (iv) fail either the area check or the edge-matching check, since their cut boundaries do not align with the boundary shown in Panel I.
Final Answer: Option (C), shape (iii).
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