Question

In the given figure, AB is a diameter of a circle with centre O and OA = 7 cm. Find the area of the shaded region.

Answer 1

AB is the diameter of the circle.
Here,
OA = 7 cm
OB = 7 cm
OA is the radius of the circle.
∴ OA = OB = OC =OD
Also,
OA is the diameter of the smaller circle.
∴ Radius of the smaller circle = $\frac{\mathrm{OA}}{2}$= 3.5 cm
Area of the smaller circle having diameter AO = ${\mathrm{\pi r}}^2$
$$\begin{gathered} =\frac{22}{7}\times 3.5\times 3.5 \\ =38.5{\mathrm{cm}}^2 \end{gathered}$$

Area of the triangle $△$CBD = $\frac{1}{2}\times b\times h$

$$\begin{gathered} =\frac{1}{2}\times 14\times 7 \\ =49{\mathrm{cm}}^2 \end{gathered}$$

Area of the semicircle having diameter CD = $\frac{1}{2}{\mathrm{\pi r}}^2$
$$\begin{gathered} =\frac{1}{2}\times \frac{22}{7}\times 7\times 7 \\ =77{\mathrm{cm}}^2 \end{gathered}$$

Now,
Area of the shaded region = Area of the semicircle $-$ Area of the triangle $△$CBD
= 77 $-$ 49
$=28{\mathrm{cm}}^2$

Also,
Area of the full-shaded region = 28 + 38.5
= 66.5 sq cm