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 the rectangle is $20-(3.5+3.5)$ metres].

• A. $129.5m^2;48m$.
• B. $179.5m^2;48m$.
• C. $129.5c{m}^2;48m$.
• D. $129.5m^2;88cm$.

Answer 1

The correct option is A $129.5m^2;48m$.

The length of the rectangle is $20-(3.5+3.5)=13m$

The breadth of the rectangular portion $=$ Diameter of the semicircle $=7m$

Area of the rectangular portion $=$ length $\times$ breadth

Area of the semicircular region $=\frac{\pi r^2}{2}$

where, radius of the semicircular region, $r=\frac{7}{2}=3.5m$

Total area of the garden $=$ Area of the rectangular portion $+$ The sum of the areas of the pair of semi circles
$=(13\times 7)m^2+\left(\begin{array}{c}2\times \frac{1}{2}\times \frac{22}{7}\times 3.5\times 3.5\end{array}\right)m^2$

$=(91+38.5)m^2$

$=129.5m^2$.

Perimeter of the garden $=2\times$ length of rectangular portion $+$ circumference of the circle

$=\left(\begin{array}{c}2\times 13)+(2\times \frac{22}{7}\times 3.5\end{array}\right)m$ [$\because$ Circumference of $2$ semicircle $=$ circumference of a circle $=2\pi r$ ]

$=(26+22)m=48m$.