Question

Find the area of the shaded region if ABCD is a rectangle with sides 8 cm and 6 cm and O is the center of the circle. (Take $\pi =3.14$)

Answer 1

Hint: As we can see a rectangle is inside the circle. Now the area of the shaded region can be calculated by subtracting the area of the rectangle from the area of the circle.

Complete step-by-step answer:
Given,
ABCD is a rectangle with sides AD=6 cm and DC=8 cm
Therefore,
Area of rectangle$=AD\times DC=6\times 8=48\text{ c}{\text{m}}^2$
Now, it is given that O is the center of the circle as AC is the diameter of the circle.
From figure $△ADC$ is a right angle triangle.
$$\begin{gathered} \Rightarrow A{C}^2=A{D}^2+D{C}^2 \\ \Rightarrow A{C}^2=6^2+8^2=100 \\ \Rightarrow AC=10 \end{gathered}$$
Therefore, radius of circle is OC(r)$={\displaystyle \frac{AC}{2}}=5$
Now, Area of circle$=\pi r^2=3.14\times 5^2=78.5\text{ c}{\text{m}}^2$
Therefore,
Area of shaded region = Area of circle –Area of rectangle
                                        $$\begin{gathered} =78.5-48 \\ =30.5\text{ c}{\text{m}}^2 \end{gathered}$$
So this is your desired answer.

Note: In this type of question first calculate the area of all the shapes given, then subtract the unwanted area, and always remember the area formulas of all standard shapes.