A plot is in the form of a rectangle ABCD having semi-circle on BC as shown in Fig. 20.23.

Question:

A plot is in the form of a rectangle ABCD having semi-circle on BC as shown in Fig. 20.23. If AB = 60 m and BC = 28 m, find the area of the plot.

Solution:

The given figure has a rectangle with a semicircle on one of its sides.

Total area of the plot $=$ Area of rectangle $\mathrm{ABCD}+$ Area of semicircle with radius $\left(\mathrm{r}=\frac{28}{2}=14 \mathrm{~m}\right)$

$\therefore$ Area of the rectangular plot with sides $60 \mathrm{~m}$ and $28 \mathrm{~m}=60 \times 28=1680 \mathrm{~m}^{2} \quad \ldots$ (i)

And, area of the semicircle with radius $14 \mathrm{~m}=\frac{1}{2} \pi \times(14)^{2}=\frac{1}{2} \times \frac{22}{7} \times 14 \times 14=308 \mathrm{~m}^{2} \quad \ldots$ (ii)

$\therefore$ Total area of the plot $=1680+308=1988 \mathrm{~m}^{2} \quad \ldots($ from (i) and (ii))

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