Question

A playground has the shape of a rectangle, with two semi-circles on its smaller sides as diameters, added to its outside. If the sides of the rectangle are 36 m and 24.5 m, find the area of the playground. (Take π = 22/7).

Answer 1

$$\begin{gathered} \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the}\mathrm{playground}\mathrm{is}\mathrm{in}\mathrm{the}\mathrm{shape}\mathrm{of}\mathrm{a}\mathrm{rectangle}\mathrm{with}\mathrm{two}\mathrm{semicircles}\mathrm{on}\mathrm{its}\mathrm{smaller}\mathrm{sides}. \\ \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{portion}\mathrm{is}36\mathrm{m}\mathrm{and}\mathrm{its}\mathrm{width}\mathrm{is}24.5\mathrm{m}\mathrm{as}\mathrm{shown}\mathrm{in}\mathrm{the}\mathrm{figure}\mathrm{below}. \end{gathered}$$


$$\begin{gathered} \mathrm{Thus},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{playground}\mathrm{will}\mathrm{be}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{a}\mathrm{rectangle}\mathrm{and}\mathrm{the}\mathrm{areas}\mathrm{of}\mathrm{the}\mathrm{two}\mathrm{semicircles}\mathrm{with}\mathrm{equal}\mathrm{diameter}24.5\mathrm{m}. \\ \mathrm{Now},\mathrm{area}\mathrm{of}\mathrm{rectangle}\mathrm{with}\mathrm{length}36\mathrm{m}\mathrm{and}\mathrm{width}24.5\mathrm{m}: \\ \mathrm{Area}\mathrm{of}\mathrm{rectangle}=\mathrm{length}\times \mathrm{width} \\ =36\mathrm{m}\times 24.5\mathrm{m}\mathrm{} \\ =882{\mathrm{m}}^2 \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{semicircle}=\mathrm{r}=\frac{\mathrm{diameter}}{2}=\frac{24.5}{2}=12.25\mathrm{m} \\ \therefore \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{semicircle}=\frac{1}{2}{\mathrm{\pi r}}^2 \\ =\frac{1}{2}\times \frac{22}{7}\times (12.25{)}^2 \\ =235.8{\mathrm{m}}^2 \\ \therefore \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{complete}\mathrm{playground}=\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{ground}+2\times \mathrm{area}\mathrm{of}\mathrm{a}\mathrm{semicircle} \\ =882+2\times 235.8 \\ =1353.6{\mathrm{m}}^2 \end{gathered}$$