Question

A plot is in the form of a rectangle ABCD having semi-circle on BC as shown in Fig. 20.23. If AB = 60 m and BC = 28 m, find the area of the plot.

Answer 1

$\text{The given figure has a rectangle with a semicircle on one of its sides.}$



$$\begin{gathered} \mathrm{Total}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{plot}=\mathrm{Area}\mathrm{of}\mathrm{rectangle}\mathrm{ABCD}+\mathrm{Area}\mathrm{of}\mathrm{semicircle}\mathrm{with}\mathrm{radius}(\mathrm{r}=\frac{28}{2}=14\mathrm{m}) \\ \therefore \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{plot}\mathrm{with}\mathrm{sides}60\mathrm{m}\mathrm{and}28\mathrm{m}=60\times 28=1680{\mathrm{m}}^2...\left(\mathrm{i}\right) \\ \mathrm{And},\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{semicircle}\mathrm{with}\mathrm{radius}14\mathrm{m}=\frac{1}{2}\mathrm{\pi }\times (14{)}^2=\frac{1}{2}\times \frac{22}{7}\times 14\times 14=308{\mathrm{m}}^2...(\mathrm{ii}) \\ \therefore \mathrm{Total}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{plot}=1680+308=1988{\mathrm{m}}^2...(\mathrm{from}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right)) \end{gathered}$$