Question

Question 3
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 meters)]

Answer 1

Given Total length = 20 m Diameter of semi circle = 7m
$\therefore$ Radius of semi circle = $\frac{7}{2}=3.5m$
Length of rectangular field = 20 - (3.5+3.5) = 20 - 7 = 13 m
Breadth of the rectangular field = 7m

Area of garden = Area of rectangular field + Area of the two semi-circular ends.

$\therefore$ Area of rectangular field = $l\times b=13\times 7=91m^2$
Area of two semi circles = $2\times \frac{1}{2}\pi r^2=2\times \frac{1}{2}\times \frac{22}{7}\times 3.5\times 3.5=38.5m^2$
Area of garden = $91+38.5=129.5m^2$

Perimeter of garden = $2\times$ length of the rectangular field + $2\times$ length of the semi-circular arcs.

Now Perimeter of two semi cricles = $2\times \pi r=2\times \frac{22}{7}\times 3.5=22m$
And Perimeter of garden = 22 + 13 + 13 = 48 m