Area and Perimeter of a Composite Beanie Shape

Area and Perimeter of a Composite Beanie Shape

Secondary 1

The diagram below shows a piece of baby beanie when flattened completely. The shaded part is made up of a trapezium and a rectangle, and the unshaded parts are two identical semicircles each with diameter \(3.5\) cm.
Find the

  1. area of the beanie. \(\left( \mathrm{Take \ }\pi \mathrm{ \ to \ be \ }\frac{\mathrm{22}}{\mathrm{7}} \right)\).
  2. perimeter of the beanie. \(\left( \mathrm{Take \ }\pi \mathrm{ \ to \ be \ }\frac{\mathrm{22}}{\mathrm{7}} \right)\).

Source consistency note: the equal semicircle diameters make the trapezium legs both 3.5 cm. With bases 9 cm and 3.5 cm and height 2 cm, those legs would instead be \(\sqrt{2^2+2.75^2}\approx3.40\text{ cm}\). The intended formula results below use the printed component dimensions; the exact measurements conflict.

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Answer:Using the printed component dimensions: (a) \(40.125\text{ cm}^2\); (b) \(27.5\text{ cm}\). The exact source dimensions conflict.

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