The figure is formed by 3 identical quarter circles and a triangle. The radius of each quarter circle is 8 cm. Find the area of the figure. (Leave your answer in terms of π\pi)

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Worked solution

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1. Calculate the area of the 3 identical quarter circles.

Area of 3 quarter circles=3×14×π×82=3×16π=48π cm2\text{Area of 3 quarter circles} = 3 \times \frac{1}{4} \times \pi \times 8^2 = 3 \times 16\pi = 48\pi\text{ cm}^2

2. Calculate the area of the right-angled triangle.

Area of triangle=12×8×8=32 cm2\text{Area of triangle} = \frac{1}{2} \times 8 \times 8 = 32\text{ cm}^2

3. Find the total area of the figure.

Total Area=48π+32 cm2\text{Total Area} = 48\pi + 32\text{ cm}^2

Answer

(48π+32) cm2(48\pi + 32)\text{ cm}^2

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