**Q) **PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semi-circles are drawn such that PQ = QR = RS. Semicircles are drawn on PQ and QS as diameters as shown in figure. Find the perimeter and area of the shaded region.

**Ans: **

Given that the radius = 6 cm

∴ Diameter PQRS = 2 x 6 = 12 cm

Since PQRS = PQ + QR + RS and its given that PQ = QR = RS

∴ 12 = 3 PQ

∴ PQ = = 4 cm

∴ PQ = QR = RS = 4 cm

**Let’s start with calculating Perimeter of Shaded region:**

∵ We know that the perimeter of a circle is given by = 2 π r or π d

∴ the perimeter of a half circle is given by: π r or π

Now the Perimeter of shaded region = Perimeter of Semi-circle of dia. PS + Perimeter of Semi-circle of dia. PQ + Perimeter of Semi-circle of dia. QS

= π + π + π

Here PS = 12 cm, PQ = 4 cm, QS = QR + RS = 4 + 4 = 8 cm

∴ Perimeter of shaded region = π + π + π

= 6 π + 2 π + 4 π = 12 π

= 12 x = = 37.714

**∴ Perimeter of shaded region = 37.714 cm**

**Next, we will calculate Area of the Shaded region:**

∵ We know that the area of a circle is given by = π r^{2} or π

∴ the area of a half circle is given by: π or π

Area of shaded region = Area of Semi-circle of dia. PS + Area of Semi-circle of dia. PQ – Area of Semi-circle of dia. QS

∴ Area of shaded region = π + π – π

Here PS = 12 cm, PQ = 4 cm, QS = 8 cm

∴ Area of shaded region = π + – π

= π

= π

= 12 π = 12 x = = 37.714

**∴ Area of shaded region = 37.714 cm ^{2}**