In the given figure, square ABCD is inscribed in the sector A - PCQ. The radius of sector C - BXD is 20 cm. Complete the following activity to find the area of shaded region

#### Solution

Side of square ABCD = radius of sector C-BXD = 20 cm

Area of square = (side)^{2} = 20^{2 }= 400 cm^{2 }

Area of shaded region inside the square

= Area of square ABCD − Area of sector C-BXD

= **400** \[- \frac{\theta}{360° } \times \pi r^2\]

= **400** \[- \frac{90° }{360° } \times \frac{3 . 14}{1} \times \frac{400}{1}\]

= **400** - 314

=** 86** cm^{2}

Radius of bigger sector = Length of diagonal of square ABCD = \[20\sqrt{2}\] cm

Area of the shaded regions outside the square

= Area of sector A-PCQ − Area of square ABCD

= A(A-PCQ) − A( ABCD )

= \[\frac{\theta}{360° } \times \pi \times r^2\] - 20^{2 }

^{ }= \[\frac{90°}{360°} \times 3 . 14 \times \left( 20\sqrt{2} \right)^2\] - (20)^{2 }

= 628 - 400

= 228 cm^{2 }

∴ Total surface area of the shaded region = 86 + 228 = 314 cm^{2}