Question

The shape of a garden is rectangular in the middle and semi circular ends as shown in the diagram. Find the area and the perimeter of this garden.

Answer 1

Given:

In rectangular garden,

Total length $=20m$

Diameter of semi circle $\left(d\right)=7m$

Radius of semi circle $\left(r\right)=\frac{7m}{2}=3.5m$

Length of rectangular field

$=20m–(3.5m+3.5m)=20m–7m=13m$

Breadth of the rectangular field $=$Diameter of semi circle $=7m$

Area of rectangular field $=\text{length}\times \text{breadth}$

$=13m\times 7m=91m^2$

Therefore, Area of rectangular field $=91m^2$---(1)

In semi-circle,

Radius $\left(r\right)=\frac{7}{2}m$

$\Rightarrow$ Area of semi circle $=\frac{1}{2}\pi r^2$

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

$=\frac{1}{1}\times \frac{11}{1}\times \frac{1}{2}m\times \frac{7}{2}m$

$=\frac{77}{4}{m}^2$

$\Rightarrow$ Area of two semi circles $=2\times \frac{77}{4}{m}^2$

$=\frac{77}{4}{m}^2$

$=38.5m^2$

So, Area of two semi circles $=38.5m^2$ ---(2)

Therefore, Area of garden $=91m^2+38.5m^2=129.5m^2$---(i)

Now

Circumference of semi circle $=\pi r$ [Since, half of the circumference of circle]

$=\frac{22}{7}\times \frac{7}{2}m$

$=11m$

$\Rightarrow$ Circumference of two semi circles $=2\times 11m=22m$---(3)

Now,

Perimeter of garden $=$ Circumference of two semi circles $+2\times$ Length of the rectangle

$=22m+2\times 13m$

$=22m+26m$

$=48m$

Therefore, Perimeter of garden $=48m$---(ii)

Hence, the area and the perimeter of garden are $129.5m^2$ and $48m$ respectively.