If a wire is bent into the shape of a square, then the area enclosed by the square is 81 cm square. When the same wire is bent into semi-circle. Find the area enclosed by the semi-circle.
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Area Of square a^2 = 81 ====> a = 9
The wire when bent in a form of Square i.e. the total perimeter of the square
Therefore,Perimeter of Square = 4a = 4*9 = 36 which is total length of the wire
the wire which is bent in the form of semicircle forms circumference of semicircle
therefore circumference is 22/7r+2r = 36 where 'r' is radius
(22+14)*r/7 = 36
r = 7 cm
Therefore area of semicircle is {(22/7)r^2}/2 = (1/2)*(22/7)*7*7
By simplifying
we get Area of semicircle = 77 cm^2
Area Of square a^2 = 81 ====> a = 9
The wire when bent in a form of Square i.e. the total perimeter of the square
Therefore,Perimeter of Square = 4a = 4*9 = 36 which is total length of the wire
the wire which is bent in the form of semicircle forms circumference of semicircle
therefore circumference is 22/7r+2r = 36 where 'r' is radius
(22+14)*r/7 = 36
r = 7 cm
Therefore area of semicircle is {(22/7)r^2}/2 = (1/2)*(22/7)*7*7
By simplifying
we get Area of semicircle = 77 cm^2