Question

In the adjoining figure, the points A, B and C are centres
of arcs of circles of radii 5 cm, 3 cm and 2 cm respectively. Find the
perimeter and the area of the shaded region. (Leave the answer in π)
​

Answer 1

THIS IS THE ANSWER TO YOUR QUESTION

Answer 2

$CD = 2 \:cm , AD = 2 + 2 + 1 = 5 \:cm ,\\BE = 3 \:cm$

$Area \: of \:the \: shaded \:region \\= \frac{pi \times CD^{2}}{2} + \Big ( \frac{\pi\times AD^{2}}{2} - \frac{\pi\times BE^{2}}{2} \Big) \\= ( CD^{2} + AD^{2} - BE^{2})\times \frac{\pi}{2}\\= ( 2^{2} + 5^{2} - 3^{2})\times \frac{\pi}{2}\\= ( 4+25-9)\times \frac{\pi}{2} \\= \frac{20}{2} \times \pi \\= 10\pi$

Therefore.,

$\red {Area \: of \:the \: shaded \:region}\green {=10\pi }$

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