Composite Figures, SM-Bank 025

A guitar plectrum was made using a semicircle and a quadrant as shown in the diagram below.

Calculate the perimeter of the plectrum, correct to the one decimal place. (2 marks)

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\(8.3\ \text{cm (1 d.p.)}\)

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\(\text{Radius of quadrant}=2\ \text{cm, Diameter of semicircle}=2\ \text{cm}\)

\(\text{Perimeter}\)	\(=1\ \text{straight edge}+\dfrac{1}{4}\times \text{circumference(1)} +\dfrac{1}{2}\times \text{circumference(2)}\)
	\(=2+\Bigg(\dfrac{1}{4}\times 2\pi r\Bigg)+\Bigg(\dfrac{1}{2}\times \pi d\Bigg)\)
	\(=2 +\Bigg(\dfrac{1}{4}\times 2\pi \times 2\Bigg)+\Bigg(\dfrac{1}{2}\times \pi\times 2\Bigg)\)
	\(=2+\dfrac{4\pi}{4}+\dfrac{2\pi}{2}\)
	\(=2+2\pi\)
	\(=8.283\dots\)
	\(=8.3\ \text{cm (1 d.p.)}\)