Question

Four equal circles are described about the four corners of a square so that each circle
touches two of the others. Find the area of the space enclosed between the circumferences
of the circles, each side of the square measuring 24 cm.
​

Answer 1

Answer:

The side of Square is given by 24cm

Area of Square is a

2

=24

2

=576cm

2

The Radius of the 4 circles at corners of square is given by

2

24

=12

The Area of quadrant of circle in side the Square is

4

1

×π×r

2

Since there are 4 such quadrants ⟹4×

4

1

πr

2

=πr

2

⟹π(12)(12)=144π=3.14(144)=452.16

So the area of remaining portion is 576−452.16=123.84