Question

calculate the area of the shaded part of the given figure​

Answer 1

Answer:

If they are tethered at the corners they can map out quarter circles within the square. For these to be maximised without sharing the quarter circles must have a radius of

1

2

of one side of the square, 25m.

Now we have four quarter circles about each corner, touching at the middle of each side.

From here we know that the full area of the field is

50

×

50

=

2500

m

2

We can calculate the grazed area as 1 circle of radius 25m

(

4

×

1

4

c

i

r

c

l

e

s

)

The area of this is equal to

π

×

r

2

=

3.14

×

25

×

25

=

1963.50

m

2

Now the ungrazed area is the total minus the ungrazed

=

2500

−

1963

=

537

m

2