Question

From a rectangular sheet of paper ABCD with AB = 40 cm and AD = 28 cm, a semicircular portion with BC as diameter is cut off. Find
the area of the remaining paper. [CBSE 2012]

Answer 1

We know that the opposite sides of rectangle are equal
∴ AD = BC = 28 cm
Now, Radius of semicircular portion = $\frac{1}{2}\mathrm{BC}=14\mathrm{cm}$
∴ Area of remaining paper = Area of rectangular sheet −Area of semicircular portion
$$\begin{gathered} =40\times 28-\frac{1}{2}\left(\frac{22}{7}\times 14\times 14\right) \\ =1120-308 \\ =812{\mathrm{cm}}^2 \end{gathered}$$
Hence, the area of the remaining paper is 812 cm²