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 semicircle whose diameter EF, LMNO is a square. What is the area (in cm2) of the shaded region?

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 semicircle whose diameter EF, LMNO is a square. What is the area (in cm²) of the shaded region?

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& \text{Area of square}={\left(14\right)}^2=196\\ & \text{Area of semicircle}=\frac{\pi }{2}{\left(7\right)}^2=\frac{49}{2}\pi \\ & \text{Side of square LMNO}=\frac{\text{diagonal}}{\sqrt{2}}=\frac{7}{\sqrt{2}}\\ & \text{Area of square LMNO}={\left(\frac{7}{\sqrt{2}}\right)}^2=\frac{49}{2}\\ & \text{Shaded portion}=196-\frac{49}{2}\pi -\frac{49}{2}\\ & =196-\frac{49}{2}\times \frac{22}{7}-\frac{49}{2}\\ & =119-\frac{49}{2}\\ & =\frac{189}{2}\\ & =94.5\end{array}$$