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Composite Figures, SM-Bank 013 MC

Grant cut two semicircles from a rectangle to create Shape 1.

He then joins the semicircles to each end of an identical rectangle to create Shape 2.

Which of the following statements is true about Shape 1 and Shape 2?

  1. They have the same area and the same perimeter.
  2. They have different areas and the same perimeter.
  3. They have the same area and different perimeters.
  4. They have different areas and different perimeters.
Show Answers Only

\(B\)

Show Worked Solution

\(\text{The semi-circles in both shapes have the same diameters}\)

\(\text{but have been turned inward in Shape 2.}\)

\(\therefore\ \text{They have different areas and the same perimeter.}\)

\(\Rightarrow B\)