PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semicircles are drawn with PQ and QS as diameters, as shown in the given figure. If PS = 12 cm, find the perimeter and area of the shaded region.
Perimeter (circumference of the circle) = 2πr
Perimeter of a semicircular arc = πr
For the arc PTS, radius is 6 cm.
∴ Circumference of the semicircle PTS =πr = 6π cm
For the arc QES, radius is 4 cm.
∴ Circumference of the semicircle QES = πr = 4π cm
For the arc PBQ, radius is 2 cm.
∴ Circumference of the semicircle PBQ = πr = 2π cm
Perimeter of the shaded region == 6π + 4π + 2π
= 12 ×3.14
= 37.68 cm
Area of the semicircle PBQ `=1/2 pi"r"^2`
= 6.28 cm2
Area of the semicircle PTS `= 1/2pi"r"^2`
= 56.52 cm2
Area of the semicircles QES `= 1/2pi"r"^2`
= 25.12 cm2
Area of the shaded region = Area of the semicircle PBQ + Area of the semicircle PTS - Area of the semicircle QES = 6.28 + 56.52 - 25.12 = 37.68 cm2