Quantitative Aptitude Ques 1546

Question: In the given figure, the side of square ABCD is 7 cm. What is the area of the shaded portion formed by the arcs BD of the circles with the centre as C and A?

Options:

A) $ 7cm^{2} $

B) $ 28cm^{2} $

C) $ 14cm^{2} $

D) $ 21cm^{2} $

Show Answer

Answer:

Correct Answer: B

Solution:

  • (b) We have, two sectors BCD and ABD. Both are symmetrical. Area of shaded portion = Area of sector BCD $ - $ Area of $ \Delta BCD $ $ =\frac{\pi r^{2}\theta }{360{}^\circ }-\frac{1}{2}\times b\times h $ $ =\frac{\pi {{(7)}^{2}}\times 90{}^\circ }{360{}^\circ }-\frac{1}{2}\times 7\times 7 $ $ =\frac{77}{2}-\frac{49}{2}=28/2sqcm $

$ \therefore $ Area of complete shaded region $ =2\times \frac{28}{2}=28cm^{2} $

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