Question

Each circle has radius 1. What is the area of the green region in the following image?

Answer 1

The area of the green section is 8 - 2(pi) as follows:

Answer 2

The big square can be cut into 4 parts such that each smaller square will have a circle in it.
the area of the smaller square = 2x2 = 4units and that of the circle is π units.
subtracting the 2 gives us double the green shaded area inside that smaller square = 4 - π units
Therefore the green shaded area in each smaller square = (4 - π)/2 units.
The total area therefore is 4 times this area = 4*(4 - π)/2 = 8 - 2π units .

Answer 3

area should be 8-2π

Comments

How did you arrive at this answer?

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take one circle and a square containing 1/4th of circle and it will also divide the associated green area in two parts. The area of this part will be 1^2(Area of the sq with side=1) -π*1^2/4(1/4th of circle area). There will be 8 such sections thus total Area will be
8-2π.