Q35 of 45 Page 12

It is proposed to add to a square lawn with the side 58m, two circular ends (the centre of each circle being the point of intersection of the diagonals of the square.) Find the area of the whole lawn [Take π=3.14]. (CBSE 2014)


ABCD is a square lawn of side 58m. AED and BFC are two circular ends.


Now, diagonal of the lawn = √(58)2 + (58)2 = 58√2m


It is given that diagonal of square = Diameter of circle


∴The radius of a circle having a centre at the point of intersection of diagonal



It is given that square ABCD is inscribed by the circle with centre O.


∴Area of 4 segments = Area of circle – Area of square


= πr2 – (side)2






m2



= 961.14m2


Area of whole lawn = Area of circle – Area of two segments



=5286.28 – 961.14


= 4325.14 m2

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