Solutions for Session 3, Part A

See solutions for Problems: A1 | A2 | A3 | A4

 Problem A1 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.

Problem A2

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

Problem A3

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

Problem A4

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