In the figure (ii) given below, area of △ABC = 35 cm². Find the area of the shaded region.

From figure,

Area of △ABC = $\dfrac{1}{2} \times$ base × height

Substituting values we get,

⇒ $\dfrac{1}{2} \times$ AB × CD = 35

⇒ $\dfrac{1}{2} \times$ AB × 5 = 35

⇒ AB = $\dfrac{35 \times 2}{5}$ = 14 cm.

From figure,

AB is the diameter of semicircle.

Radius = $\dfrac{\text{Diameter}}{2} = \dfrac{14}{2}$ = 7 cm.

Area of semi-circle = $\dfrac{πr^2}{2} = \dfrac{22}{7} \times (7)^2 \times \dfrac{1}{2}$

$= \dfrac{22}{7} \times 49 \times \dfrac{1}{2}$

= 11 × 7

= 77 cm².

Area of shaded region = Area of semi-circle - Area of △ABC

= 77 - 35

= 42 cm².

Hence, area of shaded region = 42 cm².