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).
It is given that the playground is in the shape of a rectangle with two semicircles on its smaller sides.
Length of the rectangular portion is $36 \mathrm{~m}$ and its width is $24.5 \mathrm{~m}$ as shown in the figure below.
Thus, the area of the playground will be the sum of the area of a rectangle and the areas of the two semicircles with equal diameter $24.5 \mathrm{~m}$.
Now, area of rectangle with length $36 \mathrm{~m}$ and width $24.5 \mathrm{~m}$ :
Area of rectangle $=$ length $\times$ width
$=36 \mathrm{~m} \times 24.5 \mathrm{~m}$
$=882 \mathrm{~m}^{2}$
Radius of the semicircle $=\mathrm{r}=\frac{\text { diameter }}{2}=\frac{24.5}{2}=12.25 \mathrm{~m}$
$\therefore$ Area of the semicircle $=\frac{1}{2} \pi \mathrm{r}^{2}$
$=\frac{1}{2} \times \frac{22}{7} \times(12.25)^{2}$
$=235.8 \mathrm{~m}^{2}$
$\therefore$ Area of the complete playground $=$ area of the rectangular ground $+2 \times$ area of a semicircle
$=882+2 \times 235.8$
$=1353.6 \mathrm{~m}^{2}$