In the 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 the shaded portion.

Side of the square ABCD = radius of sector C-BXD = 20 cm
Area of square `="side"^2= 400 cm^2`
Area of sector C-BXD ` = theta/360xx pir^2`
`=square/360xx3.14xx20^2=square cm^2`
Area of the shaded portion inside square
= Area of square - A (sector C- BXD)
`=400-square cm^2`
Radius of sector A-PCQ= Length of diagonal of square ABCD
`r_1=20sqrt2`cm
Area of the shaded region outside square
= A(sector A-PCQ)-A (square ABCD)
`=90/360xx3.14xx(20sqrt2)^2-200`
`= squarecm^2`
`:.` total area of shaded portion = area of shaded portion inside square + area of shaded portion outside square `= square cm^2`

Explanation

Side of the square ABCD = radius of sector C-BXD= 20 cm
Area of square `="side"^2=400cm^2`
Area of sector C-BXD` =theta/360xxpir^2`
`=90/360xx3.14xx20^2`
`=314 cm^2`
Area of the shaded portion inside square
= Area of square - A (sector C-BXD)
`= 400 -314`
`= 86 cm^2`
Radius of sector A-PCQ = Length fo diagonal of square ABCD
`=r_1=20sqrt2cm`
Area of the shaded region outside square
= A(sector A-PCQ)- A(square ABCD)
`= 90/360xx3.14xx(20sqrt2)^2-200`
`= 228 cm^2`
`:.` total area of shaded portion = area of shaded portion inside square + area of shaded portion outside square `= 314 cm^2`.