Composite Figures, SM-Bank 026

Find the exact perimeter of the composite shape below. (2 marks)

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

Show Answers Only

\(80+10\pi)\ \text{cm}\)

Show Worked Solution

\(\text{Radius of quadrant}=29\ \text{mm}\)

\(\text{Perimeter}\)	\(=4\ \text{straight edges}+\dfrac{1}{4}\times \text{circumference} \)
	\(=4\times 20+\Bigg(\dfrac{1}{4}\times 2\pi r\Bigg)\)
	\(=80 +\Bigg(\dfrac{1}{4}\times 2\pi \times 20\Bigg)\)
	\(=80+\dfrac{40\pi}{4}\)
	\(=(80+10\pi)\ \text{cm}\)