Question 5
Shapes can be made by joining diamonds edge to edge. Each diamond has equal sides, an angle of 60 degrees and an adjacent angle of 120 degrees, and area 1 square unit. Exactly two different shapes can be made from two diamonds; these are called bimonds, each of area 2 square units.
Each shape below is a trimond made from three edge-joined diamonds, of area 3 square units. The three pictures show the same trimond: rotations or reflections produce one from another.
(1) From a set of one diamond, two different bimonds and your collection of different trimonds, fit some pieces together into a parallelogram of area 12 square units. Draw it, showing the pieces used. (2 points)
(2) From the same set of pieces, make another parallelogram of area 12 square units but with a different perimeter. Draw it. (2 points)
(3) How many different shapes can be made from four diamonds joined edge to edge, each of area 4 square units? (4 points)
Each shape below is a trimond made from three edge-joined diamonds, of area 3 square units. The three pictures show the same trimond: rotations or reflections produce one from another.
(1) From a set of one diamond, two different bimonds and your collection of different trimonds, fit some pieces together into a parallelogram of area 12 square units. Draw it, showing the pieces used. (2 points)
(2) From the same set of pieces, make another parallelogram of area 12 square units but with a different perimeter. Draw it. (2 points)
(3) How many different shapes can be made from four diamonds joined edge to edge, each of area 4 square units? (4 points)