Composite Figures, SM-Bank 032

The design below is made up of one \(106^\circ\) sector arc and two right angled triangles.

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

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

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\(23.25\ \text{mm (2 d.p.)}\)

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\(\text{Radius of sector}\ r=5\ \text{m, Sector angle }\theta=106^\circ\)

\(\text{Perimeter}\)	\(=3\ \text{straight edges}+1\ \text{arc length}\)
	\(=2\times 3+8+\Bigg(\dfrac{\theta}{360}\times 2\pi r\Bigg)\)
	\(=14+\Bigg(\dfrac{106}{360}\times 2\pi\times 5\Bigg)\)
	\(=14+\dfrac{53}{18}\times \pi\)
	\(=23.2502\dots\)
	\(\approx 23.25\ \text{mm (2 d.p.)}\)