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?

Solution (By Examveda Team)

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