Question

In the shown figure, PQRS is a square of side 12 cm, and OM LSR. Find the length of MQ​

Answer 1

Step-by-step explanation:

Let its diagonals intersect at O.

Then, OP=OQ=OR=OS

and

∠

P

O

S

=

∠

Q

O

R

=

90

∘

P

R

2

=

P

Q

2

+

Q

R

2

P

R

=

(

√

2

×

42

)

m

Now, OP=

1

2

×

(

d

i

a

g

o

n

a

l

)

=

21

√

2

m

∵

Area of flower bed PAS=Area of flower bed QBR

∵

Total Area of the two flower beds=Area of flower bed PAS+Area of flower bed QBR

=

2

×

[

Area of sector OPAS-Area of

△

P

O

S

]

=

2

×

[

π

r

2

θ

360

∘

−

1

2

×

O

P

×

O

Q

]

=

2

×

[

π

r

2

θ

360

∘

−

1

2

r

2

]

[

w

h

e

r

e

,

θ

=

90

∘

]

=

2

×

[

22

7

×

(

21

√

2

)

2

90

∘

360

∘

−

1

2

×

21

√

2

×

21

√

2

]

[

∵

s

i

n

90

∘

=

1

]

=

2

×

[

22

7

×

21

×

21

×

2

×

1

4

−

1

2

×

21

×

21

×

2

]

=

2

[

33

×

21

−

441

]

=2[693-441]

=

504

m

2

Hence area of flower beds is

504

m

2

.