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. [Take π = 3.14.]

Here we will subtract the area of semicircle whose diameter is QS from the area of the semicircle whose diameter PS and add the area of semicircle whose diameter is PQ so as to find out the area of the shaded region.


Given PS = 12 cm


Radius of the circle = 6 cm


PQ = QR = RS


So let PQ = QR = RS = k cm


Also, PQ + QR + RS = PS


k + k + k = 12


3k = 12



k = 4 cm


So, PQ = QR = RS = 4 cm



Area and perimeter of semicircle whose diameter is PS




Radius = 6 cm



Area of semicircle = 18π cm2 eqn2


Perimeter of semicircle = πr


Perimeter of semicircle = π×6


Perimeter of semicircle = 6π cm eqn3


Area of semicircle whose diameter is QS




Radius = 4 cm



Area of semicircle = 8π cm2 eqn4


Perimeter of semicircle = πr


Perimeter of semicircle = π×4


Perimeter of semicircle = 4π cm eqn5


Area of semicircle whose diameter is PQ




Radius = 2 cm



Area of semicircle = 2π cm2 eqn6


Perimeter of semicircle = πr


Perimeter of semicircle = π×2


Perimeter of semicircle = 2π cm eqn7


Area of the shaded region = eqn2 – eqn4 + eqn6


Area of shaded region = 18π – 8π + 2π


Area of shaded region = 12π


Area of shaded region = 12×3.14 (putting π = 3.14)


Area of shaded region = 37.68 cm2


Perimeter of shaded region = eqn3 – eqn5 + eqn7


Perimeter of shaded region = 6π -4π + 2π


Perimeter of shaded region = 4π


Perimeter of shaded region = 4×3.14 (put π = 3.14)


Perimeter of shaded region = 12.56 cm


Perimeter of the shaded region is 12.56 cm and Area of shaded region is 37.68 cm2.


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