#### 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 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))

Is there an error in this question or solution?

Solution 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. Concept: Introduction of Mensuration.