Question

To decompose a quadrilateral into two identical shapes, Clare drew a dashed line as shown in the diagram.

1. She said that two resulting shapes have the same area. Do you agree? Explain your reasoning.
Did Clare partition the figure into two identical shapes? Explain your reasoning.

Answer 1

• 1. Figures are of same area
• 2. Figures are of different shape

Explanation:

See attached

The figure in the graph is trapezium

1..................................................

The two shapes have an area of

Triangle:

• A = 1/2bh = 1/2*4*4 = 8 square units

Rectangle:

• A = wl = 2*4 = 8 square units

2..................................................

The two partitions are not identical in shape as one of them is triangle and the other is rectangle