Composite Figures, SM-Bank 019 MC

The courtyard shown below incorporates quadrants and rectangles in its design.

The landscaping company needs to calculate the perimeter of the courtyard so they can provide estimates for fencing.

Which answer represents the approximate length of fencing required, to the nearest metre?

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\(D\)

Show Worked Solution

\(\text{Radius}=4+2=6\ \text{m}\)

\(\text{Perimeter}\)	\(=6\ \text{straight sides}+2\ \text{quadrants}\)
	\(=2\times 4+2\times 8+ 2\times 2+\Bigg(2\times \dfrac{1}{4}\times 2\pi r\Bigg)\)
	\(=28+\pi\times 6\)
	\(=46.849\dots\)
	\(\approx 47\ \text{m (nearest metre)}\)

\(\Rightarrow D\)