Question

Find the area of Fig. 20.25, in square cm, correct to one place of decimal. (Take π = 22/7)

Answer 1

$\text{The given figure is:}$



$$\begin{gathered} \mathrm{Construction}:\mathrm{Connect}\mathrm{A}\mathrm{to}\mathrm{D}. \\ \mathrm{Then},\mathrm{we}\mathrm{have}:\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{figure}=(\mathrm{Area}\mathrm{of}\mathrm{rectangle}\mathrm{ABCD}+\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{semicircle})-(\mathrm{Area}\mathrm{of}∆\mathrm{AED}). \\ \therefore \mathrm{Total}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{figure}=(\mathrm{Area}\mathrm{of}\mathrm{rectangle}\mathrm{with}\mathrm{sides}10\mathrm{cm}\mathrm{and}10\mathrm{cm})+(\mathrm{Area}\mathrm{of}\mathrm{semicircle}\mathrm{with}\mathrm{radius}=\frac{10}{2}=5\mathrm{cm})-(\mathrm{Area}\mathrm{of}\mathrm{triangle}\mathrm{AED}\mathrm{with}\mathrm{base}6\mathrm{cm}\mathrm{and}\mathrm{height}8\mathrm{cm}\mathrm{)} \\ =(10\times 10)+(\frac{1}{2}\times \frac{22}{7}\times 5^2)-(\frac{1}{2}\times 6\times 8) \\ =100+39.3-24 \\ =115.3{\mathrm{cm}}^2 \end{gathered}$$