In the figure (i) given below, the points A, B and C are centres of arcs of circles of radii 5 cm, 3 cm and 2 cm respectively. Find the perimeter and the area of the shaded region. (Take π = 3.14)

Let r₁ = 5 cm, r₂ = 3 cm and r₃ = 2 cm.

Perimeter of shaded region = Circumference of largest semi-circle + Circumference of smaller semi-circle + Circumference of smallest semi-circle

= πr₁ + πr₂ + πr₃

= π(5 + 3 + 2)

= 10π

= 10 x 3.14

= 31.4 cm.

Area of shaded region = Area of largest semi-circle - Area of smaller semi-circle + Area of smallest semi-circle

$= \dfrac{πr$1^2}{2} - \dfrac{πr2^2}{2} + \dfrac{πr3^2}{2} \\[1em] = π\Big(\dfrac{r1^2}{2} - \dfrac{r2^2}{2} + \dfrac{r3^2}{2}\Big) \\[1em] = 3.14\Big(\dfrac{5^2}{2} - \dfrac{3^2}{2} + \dfrac{2^2}{2}\Big) \\[1em] = 3.14\Big(\dfrac{25}{2} - \dfrac{9}{2} + \dfrac{4}{2}\Big) \\[1em] = 3.14\Big(\dfrac{25 - 9 + 4}{2} \Big) \\[1em] = 3.14\Big(\dfrac{20}{2} \Big) \\[1em] = 3.14\times 10 \\[1em] = 31.4 \text{ cm}^2.

Hence, perimeter of shaded region = 31.4 cm and area of shaded region = 31.4 cm².