Question : In the given figure, ABCD is a square of side 14 cm. E and F are mid-points of sides AB and DC respectively. EPF is a semi-circle whose diameter is EF. LMNO is square. What is the area (in cm2) of the shaded region?
Option 1: 108.5
Option 2: 94.5
Option 3: 70
Option 4: 120
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Correct Answer: 94.5
Solution :
Given that ABCD is a square of side 14 cm.
The area of the semicircle = $\frac{\pi r^2}{2}$ = $\frac{\pi (7)^2}{2}$ = 77 cm
2
Since the radius of the semicircle is equal to the diagonal of a smaller square.
The diagonal of a square = 7 cm
The side of a smaller square = $\frac{7}{\sqrt2}$ cm
The area of a smaller square = $\frac{49}{2}$ cm
2
The area of a bigger square = 14
2
= 196 cm
2
The area of the shaded region = The area of a bigger square – The area of a smaller square – The area of the semicircle
The area of the shaded region = 196 – 77 – $\frac{49}{2}$ = 94.5 cm
2
Hence, the correct answer is 94.5.
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