Question

29
sides of a square lawn ABCD of side 56 m. If the centre of each circular flower bed
is the point of intersection O of the diagonals of the square lawn, find the sum of
the areas of the lawn and the flower beds.
(a) In the figure (i) given below, two circular flower beds have been shown on the two​

Answer 1

Step-by-step explanation:

ANSWER

Side of square ABCD=56 m

AC=BD(diagonals of a square are equal in lengths)

Diagonal of square (AC) =

2

× side square

=

2

×56=56

2

m

OA=OB=

2

1

AC=

2

1

(56

2

)=28

2

m

Let OA=OB=r m[radius of the sector]

Area of sector OAB=[

360

o

90

o

]πr

2

=(

4

1

)πr

2

=

4

1

×

7

22

×(

2

28

)

2

m

2

=[

4

1

×

7

22

×28×28×2] m

2

=1232 m

2

Area of flower bed AB=area of sector OAB− area of ΔOAB

⇒1232−

2

1

×OB×OA⇒1232−

2

1

×28

2

×28

2

⇒1232−784=448m

2