21. If a wire is bent in the shape of a square, the area of the square is 81 cm?. When the same wire is bent into the form of a semicircular arc bounded by its diameter, find the area of the shape so formed. (take π = 22/7).
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Let the side of the square be a cm
Thus, perimeter is 4a and area of the square is a2
∴a^2=81
⇒a=81
⇒a=9
Thus, perimeter =4×9 =36 cm
Now, wire is bent into a semicircle.
Therefore, 2r+πr=36
⇒r(π+2)=36
⇒r=722+236
⇒r=73636
⇒r=7 cm
Area of semicircle =21πr2
=21×722×7×7
=77 cm^2
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