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].

Total length = 20 m 

Diameter of semi circle = 7 m 

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

Length of the rectangle$= 20 – (3.5 + 3.5) = 20 – 7 = 13 m$

Breadth of the rectangular field = 7 m

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

Area of two semi circular ends $= 2\left(\frac{1}{2}\pi r^2\right)$
Area of two semi circular ends$= \mathrm{\pi }{r}^2 = \frac{22}{7} \times 7^2 \times 7^2 =\frac{77}{2} m^2 = 38.5 m^2$

Total area = Area of the rectangular field  + Area of two ends $= 91 m^2 + 38.5 m^2 = 129.5 m^2$

Total perimeter = Perimeter of the rectangle + Perimeter of two ends
$= 2 (l + b) + 2 \times \left(\pi r\right) – 2\left(2r\right)$
$= 2 (13 + 7) + 2(\frac{22}{7}\times \frac{7}{2}) – 4\times \frac{7}{2}$
$= 2 \times 20 + 22 – 14 = 40 + 22 – 14 = 48 m$