Question

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

• A. 129.5 sq.m.
• B. 128.5 sq.m.
• C. 138.5 sq.m.
• D. 122.5 sq.m.

Answer 1

Answer: (A)

The. given figure has a rectangle and two semicircles.

Clearly, the diameter of each semi-circle is $7m$

$\Rightarrow$ radius of the semi-circle $\left(r\right)=\frac{7}{2}m$

Area of rectangular part = Length $\times$ Width

Length $=$ Total length of the figure $-$ $2\times$ radius of semi-circle

Length $=20m-(2\times \frac{7}{2}m)=(20m-7m)=13m$

Width of the rectangle $=$ diameter of semi-circle $=7m$

$\Rightarrow$ Area of rectangle $=(13\times 7)sq.m=91sq.m$

Here, we have two semi circular portions with the same radius $\frac{7}{2}m$.

Also, area of semi-circular portion $=2\times$ Area of semicircle

$=2\times \frac{\pi r^2}{2}$

$=\pi r^2$

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

$=38.5sq.m$

Total area $=91sq.m+38.5sq.m=129.5sq.m$