In the figure given below ABCD is a square of side 4 cm Quadrants of a circle of diameter 2 cm are r...........

Quantitative Aptitude (CDS) Mensuration 2D

In the figure given below, ABCD is a square of side 4 cm. Quadrants of a circle of diameter 2 cm are removed from the four corners and a circle of diameter 2 cm is also removed. What is the area of the shaded region?

$\small 5\frac{7}{9} \: cm^{2}$

$\small \small 7\frac{7}{9} \: cm^{2}$

$\small \small 9\frac{5}{7} \: cm^{2}$

$\small \small \small 9\frac{5}{6} \: cm^{2}$

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Explanation:

Area of shaded region = Area of square – area of circle – 4 x area of quadrant
= side² - $\small \pi$ r² - 4x(1/4) $\small \pi$ r²
= 4² - $\small \pi$ (1)² - $\small \pi$ (1)² = 16 - 44/7 = 9(5/7) cm²