Composite Figures, SM-Bank 029

Jonti is constructing the stage for the local music festival. The design is made up of one \(60^\circ\) sector arc and two equilateral triangles.

Calculate the perimeter of Jonti's stage. Give your answer correct to one decimal place. (2 marks)

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

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\(25.2\ \text{m (1 d.p.)}\)

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\(\text{Radius of sector}\ r=5\ \text{m, Sector angle }\theta=60^\circ\)

\(\text{Perimeter}\)	\(=4\ \text{straight edges}+1\ \text{arc length}\)
	\(=4\times 5+\Bigg(\dfrac{\theta}{360}\times 2\pi r\Bigg)\)
	\(=20+\Bigg(\dfrac{60}{360}\times 2\pi\times 5\Bigg)\)
	\(=20+\dfrac{5}{3}\pi\)
	\(=25.235\dots\)
	\(\approx 25.2\ \text{m (1 d.p.)}\)