Composite Figures, SM-Bank 030

The design below is made up of one \(120^\circ\) sector arc and three identical rhombuses.

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

NOTE: \(\text{Arc length: }l=\dfrac{\theta}{360}\times 2\pi r\)

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\(34.0\ \text{cm (1 d.p.)}\)

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\(\text{Radius of sector}\ r=4.2\ \text{m, Sector angle }\theta=120^\circ\)

\(\text{Perimeter}\)	\(=6\ \text{straight edges}+1\ \text{arc length}\)
	\(=6\times 4.2+\Bigg(\dfrac{\theta}{360}\times 2\pi r\Bigg)\)
	\(=25.2+\Bigg(\dfrac{120}{360}\times 2\pi\times 4.2\Bigg)\)
	\(=25.2+\dfrac{1}{3}\times 8.4\pi\)
	\(=33.996\dots\)
	\(\approx 34.0\ \text{cm (1 d.p.)}\)