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 [Length of rectangle is 20 – (3.5 + 3.5) metres].

Answer 1

Given: Total length = 20 m

Diameter of semi-circle = 7 m

$\text{Radius of semi-circle}=\frac{7}{2}=3.5m$

Length of rectangular field

$=20-(3.5+3.5)=20-7=13m$

Breadth of the rectangular field = 7 m

$\text{Area of rectangular field}=l\times b$

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

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

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

$=38.5m^2$

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

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

$\text{And Perimeter of garden}=22+13+13$

$=48m.$