Q16 of 35 Page 311

The area of circular field is 154 sq cm. Let us write by calculating the perimeter and area of circumference circular field with square.


Given: Area of circle = 154 cm2


We know that


Area of a circle = πr2


⇒ πr2 = 154



⇒ r2 = 7× 7


⇒ r = 7 cm


Also, Diameter of the circle = 2× radius


⇒ CE = 2× 7 = 14 cm


This acts as the diagonal of the inscribed square.


So, the diagonal of the square BCDE= 14 cm


Let the side of the square be x cm


We know that each angle of a square is 90°.


Using Pythagoras theorem,


CD2 +DE2 = CE2


⇒x2+ x2 = 142


⇒ 2x2 = 196


⇒x2 =98


Side of the square =7√2 cm


We know that Area of a Square = side× side


⇒ Area of BCDE =98 cm2


Perimeter of a square = 4× side


⇒ Perimeter of BCDE = 4× 7√2 = 28√2 cm


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