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Solutions for Session 3, Part A
See solutions for Problems: A1 | A2 | A3 | A4
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Problem A1 | |
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The first two shapes are not polygons because they are not made of straight line segments. The third shape is not a polygon because it is not closed, while the fourth shape divides the plane into three regions, rather than two.
<< back to Problem A1
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Problem A2 | |
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There are 13 polygons. They are as follows:
• | Four small triangles, each defined by one side of the rectangle and two halves of the diagonals (e.g., XYV) |
• | Four pentagons, each a complement of one of the small triangles (e.g., VYZWX) |
• | Four large triangles, each defined by two sides of the rectangle and one of the diagonals (e.g., triangle XZW) |
• | The rectangle XYZW |
Score: (8 • 3) + (1 • 4) + (4 • 5) = 48 points
<< back to Problem A2
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Problem A3 | |
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There are 13 polygons. They are as follows:
• | Four small rectangles, all of which share the vertex Q (e.g., SMPQ) |
• | Four hexagons, each a complement of one of the small rectangles (e.g., PNOLSQ) |
• | Four larger rectangles, each defined by two small rectangles sharing one side (e.g., MNTS) |
• | The rectangle MNOL |
Score: (9 • 4) + (4 • 6) = 60 points
<< back to Problem A3
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Problem A4 | |
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There are 13 polygons. They are as follows:
• | Two small triangles (RUV and TWV) |
• | Their two complements (hexagons VUSTQR and VWQRST) |
• | Two quadrilaterals (RQWV and TSUV) |
• | Their two complements (pentagons VRSTW and VTQRU) |
• | Two larger triangles (RQT and TSR) |
• | Three rectangles (RUWQ, USTW, and QRST) |
Score: (4 • 3) + (5 • 4) + (2 • 5) + (2 • 6) = 54 points
<< back to Problem A4
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