Composite Figures, SM-Bank 031

The design below is made up of one \(40^\circ\) sector arc and a right angled triangle.

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

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

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

\(29.1\ \text{cm (1 d.p.)}\)

Show Worked Solution

\(\text{Radius of sector}\ r=13\ \text{m, Sector angle }\theta=40^\circ\)

\(\text{Perimeter}\)	\(=3\ \text{straight edges}+1\ \text{arc length}\)
	\(=12+5+13+\Bigg(\dfrac{\theta}{360}\times 2\pi r\Bigg)\)
	\(=30+\Bigg(\dfrac{40}{360}\times 2\pi\times 13\Bigg)\)
	\(=30+\dfrac{26}{9}\times \pi\)
	\(=29.075\dots\)
	\(\approx 29.1\ \text{cm (1 d.p.)}\)