(Q7) Find the area of the segments shaded in figure if PQ =24cm PR=7cm and QR is the diameter of the circle with center O (take π value)

PROQ24cm7cm

Area of the segments shaded = Area of sector OQPR - Area of triangle PQR

Since QR is diameter , ∠QPR = 90° (Angle in a semicircle)

So , using Pythagoras Theorem

In triangle QPR , QR2 = PQ2+PR2

QR2 = 2+2

  =

QR = √ = cm

Then radius of the circle =
1
2
 QR
           =
1
2
 ()=
2
 cm
Now, area of semicircle OQPR =
1
2
 πr2
              =
1
2
 ×
22
7
 ×
2
 ×
2

              = .53cm2

Area of right angled triangle QPR =
1
2
 ×PR×PQ
               =
1
2
 ××

               =cm2

Area of the shaded segments = .53 -

              = .53cm,2