Sum
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.
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Solution
The given figure has a rectangle with a semicircle on one of its sides.
Total area of the plot = Area of rectangle ABCD + Area of semicircle with radius \[(r = \frac{28}{2} = 14m)\]
∴ Area of the rectangular plot with sides 60m and\[ 28m = 60 \times 28 = 1680 m^2 . . . (i)\]
And, area of the semicircle with radius \[14m = \frac{1}{2}\pi \times (14 )^2 = \frac{1}{2} \times \frac{22}{7} \times 14 \times 14 = 308 m^2 . . . (ii)\]
∴ Total area of the plot \[ = 1680 + 308 = 1988 m^2\] . . . (from (i) and (ii))
Total area of the plot = Area of rectangle ABCD + Area of semicircle with radius \[(r = \frac{28}{2} = 14m)\]
∴ Area of the rectangular plot with sides 60m and\[ 28m = 60 \times 28 = 1680 m^2 . . . (i)\]
And, area of the semicircle with radius \[14m = \frac{1}{2}\pi \times (14 )^2 = \frac{1}{2} \times \frac{22}{7} \times 14 \times 14 = 308 m^2 . . . (ii)\]
∴ Total area of the plot \[ = 1680 + 308 = 1988 m^2\] . . . (from (i) and (ii))
Concept: Mensuration
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