Two circles of radius 2 are centred at (2,0) and at (0,2). what is the area of the intersection of the interiors of the two circles?
write steps

You first have to draw the circles and find the region of intersection which the problem cites. One circle should be on the x-axis and the other on the y-axis and the intersection should be somewhere on the 1st quadrant or the upper right quadrant.

Next, you can draw a square around the intersection region with the radii of the circles as the sides of the squares.
Then, you analyze how you can calculate for the area of the intersection.

Here is the breakdown:

The area of 1/4 of the circle inside the square can be subtracted from the square. The difference would be the area of that region inside the square but outside the intersection.
You multiply that by two to include the area of the other side. Let us call this total area as the un-included region.
Finally, we subtract the area of the un-included region from the area of the square and we get the area of the intersection.

In equation form, with A are the area:
A(intersection) = A(square) - 2 ( A(square) - A(1/4 circle) )
Simplifying this,
A(intersection) = 2 A(1/4 circle) - A(square)

Plugging in the formula for the area of the square and the circle, and the given values:
A(intersection) =