Question

The shape of a garden is rectangular in the middle and semi-circular at the ends as shown in the diagram.

Find the area and the perimeter of this garden.

Answer 1

Total length$=20\mathrm{m}$

Diameter of semi circle$=7\mathrm{m}$

Therefore, Radius of semi circle $=3.5m$

Length of rectangular field $=20–(3.5+3.5)=20–7=13\mathrm{m}$

Breadth of the rectangular field$=7\mathrm{m}$

We have to find out the perimeter and area of rectangular field

Area of rectangular field $=\mathrm{l}\times \mathrm{b}=13\times 7=91{\mathrm{m}}^2$

Area of two semi circles $=2\times \frac{1}{2}\times \mathrm{\pi }\times {\mathrm{r}}^2$

$=2\times \frac{1}{2}\times \frac{22}{7}\times 3.5\times 3.5$

$=38.5{\mathrm{m}}^2$

Area of garden $=91+38.5=129.5{\mathrm{m}}^2$

Now Perimeter of two semi circles $$\begin{gathered} =2\times \mathrm{\pi }\times \mathrm{r} \\ =2\times \frac{22}{7}\times 3.5 \\ =22\mathrm{m} \end{gathered}$$

Therefore, Perimeter of garden$=22+13+13=48\mathrm{m}$

Hence- Area of garden$=129.5{\mathrm{m}}^2$

Perimeter of garden$=48\mathrm{m}$