Question 75

In the figure, ABCD is a square with side 10. BFD is an arc of a circle with centre C. BGD is an arc of a circle with centre A. What is the area of the shaded region

Solution

Side of square = Radius of arc = 10 cm

Now, area of shaded region = $$2\times[$$ area (sector ABD) $$-$$ area ($$\triangle$$ ABD) $$]$$

= $$2\times[(\frac{\theta}{360^\circ}\times\pi r^2)-(\frac{1}{2})\times b\times h]$$

= $$2\times[(\frac{90^\circ}{360^\circ}\times\pi \times100)-(\frac{1}{2}\times 10\times 10)]$$

= $$2\times(25\pi-50)$$

= $$(50\pi-100)$$ $$cm^2$$

=> Ans - (C)

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