Question:
A plot is in the form of a rectangle ABCD having semi-circle on BC as shown in the following figure. If AB = 60 m and BC = 28 m, find the area of the plot.
Solution:
It is given that a plot is in form of rectangle ABCD having a semicircle on BC.
$\mathrm{AB}=60 \mathrm{~m}$
$\mathrm{BC}=28 \mathrm{~m}$
Since BC is the diameter of semicircle. Then, radius of semicircle is
$r=\frac{28}{2} \mathrm{~m}$
$=14 \mathrm{~m}$
Area of semicircle $=\frac{1}{2} \times \pi r^{2}$
$=\frac{1}{2} \times \frac{22}{7} \times 14 \times 14$
$=308 \mathrm{~m}^{2}$
Area of rectangle $\mathrm{ABCD}=l \times b$
$=60 \times 28$
$=1680 \mathrm{~m}^{2}$
Now,
Area of plot = Area of rectangle + Area of semicircle
$=1680+308 \mathrm{~m}^{2}$
$=1988 \mathrm{~m}^{2}$