In the given figure, PQRS is a square of diagonal `7sqrt(2)` cm. With P as the centre, the arc QS is drawn. Find the area of the shaded region (in `cm^(2)`).

Options

A. `(49)/(4)(pi-2)`
B. `(49)/(4)(pi-1)`
C. `(49)/(4)(pi-3)`
D. `(49)/(2)(pi-2)`

Answer

A

Explanation

Area of the shaded region
= Area of the sector PQS - Area of `triangle PQS`
`QS=sqrt(2)"(side)"=7sqrt(2) cm. `
Side = 7 cm
` :. ` Area of sector PQS
`=(90^(@))/(360^(@)) pi (7)^(2)=(49pi)/(4) cm^(2)`
Area of `triangle PQS =(1)/(2) (PQ) (PS)`
`=(1)/(2)(7)^(2)=(49)/(2) cm^(2)`
` :. " Required area "=((49pi)/(4)-(49)/(2))cm^(2)`
`=(49)/(4) (pi-2)cm^(2)`