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

Step-by-step explanation:

The side of square is given by 24 cm

Area of Square is a

2

=24

2

=576 cm

2

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

2

24

=12 cm

The area of quadrant of circle inside the square is

4

1

×π×r

2

Since there are 4 such quadrants so area = 4×

4

1

πr

2

=πr

2

Area of 4 quadrants=π(12)(12)=144π=3.14(144)=452.16 cm

2

So the area of the space enclosed between the circumferences of the circles = Area of Square - Area of 4 quadrants