Six different shapes are cut from a square as shown on the left. Which option(s) is/are made using only the cut pieces? Pieces can be rotated and not all pieces need to be used.
Show Hint
In Tangram dissection problems, always track the unique irregular piece (Tile 6). Because its weird angles cannot be synthesized by combining standard triangles, you must locate its exact outline inside the target silhouette first.
Step 1: Understanding the Question:
We are shown a square disassembled into six unique polygonal tiles. We must examine the four solid black silhouettes (A, B, C, D) and determine which of them can be assembled using a subset (or all) of these six specific tiles, allowing for rotation.
Step 2: Key Formula or Approach:
We inventory the precise geometric profile of the six available source tiles:
• Tile 1: A small regular square.
• Tile 2: A small right-angled triangle.
• Tile 3: Another small right-angled triangle.
• Tile 4: A medium-sized triangle.
• Tile 5: A large right-angled triangle.
• Tile 6: A large irregular non-symmetrical pentagon/quadrilateral.
We then attempt to tile the target silhouettes using these exact shapes without overlapping or altering their internal angles.
Step 3: Detailed Explanation:
• Let us evaluate
Figure A (Walking figure):
- The diamond-shaped head is formed by rotating Tile 1 (the square) by 45 degrees.
- The angular torso and stepping legs assemble cleanly by mating the long diagonal edge of Tile 5 (large triangle) against the irregular edge of Tile 6.
- The small triangles provide the extended foot and arm segments. This silhouette decomposes entirely into the available tiles. Therefore, Option A is correct.
• Let us evaluate
Figure B (Standing figure):
- The head is formed by Tile 1 in its standard unrotated orientation.
- The triangular shoulders and chest match Tile 4 and the small triangles.
- The bulky lower body and separated legs match the precise profiles of Tile 5 and Tile 6. Therefore, Option B is correct.
• Let us evaluate
Figure C (Bowing figure):
- The square head uses Tile 1.
- The pointed neck matches one of the small triangles.
- The forward-leaning torso and lower extremities map directly to the large triangle and the irregular pentagon. Therefore, Option C is correct.
• Let us evaluate
Figure D:
- This figure features a massive triangular head and elongated body proportions that require surface areas and acute angle combinations not present in our six source tiles. Attempting to fit our pieces leaves empty gaps. Therefore, Option D is incorrect.
Step 4: Final Answer:
Figures (A), (B), and (C) can be constructed using the cut pieces.
