Question

There are two circular portions on two sides of a square lawn of side 58m. The centre of each circular portion is the portion is the point of intersection of the diagonals of the square lawn.Find the area of the lawn in whole.​

Answer 1

ANSWER

Let ABCD be a square with side 58 metres

Let its diagonals intersect at O

Then OA=OB=OC=OD and

∠AOD=∠BOC=90

∘

With radius=

2

1

AC arcs have been drawn namely AED and CBF

∴Radius of each arc=

2

1

×diagonal

=

2

1

2

×58

=1.41×29=40.89metres.

58×58+2×[

7

22

×(40.89)

2

×

360

90

−

2

1

×(40.89)

2

90

∘

]

33.64+

7

11×(40.89)

2

−(40.89)

2

=(3364+2627.4−1671.9) sq metres

=4319.5 sq metres