Question

In the given figure, AOBC represents a quadrant of a circle of radius 3.5 cm with centre O. Calculate the area of the shaded portion.

Answer 1

Area of the right-angled $∆$AOD = $\frac{1}{2}\times b\times h$
=$\frac{1}{2}\times 3.5\times 2=3.5{\mathrm{cm}}^2$

Area of the sector AOB =$\frac{\theta }{360}\times \mathrm{\pi }\times r^2$
$$\begin{gathered} =\frac{90}{360}\times \frac{22}{7}\times {\left(3.5\right)}^2 \\ =9.625{\mathrm{cm}}^2 \end{gathered}$$

Area of the shaded region = Area of the $∆\mathrm{AOD}$ $-$ Area of the sector AOB

$$\begin{gathered} =9.625-3.50 \\ =6.125{\mathrm{cm}}^2 \end{gathered}$$