If we assume that the red squares measure 1x1, then the red region has an area of 10 square units.

The next step is to establish the dimensions of the blue square.

The top left and bottom left triangles in the above figure are similar, so (2+x)/1 = 2/x. Cross-multiplying and solving the resulting quadratic we find that x = sqrt3-1, or about 0.732.

Using Pythagoras the side length of the blue square is therefore sqrt(8+2sqrt3), and the area of the full square is 8+2sqrt3.

From that we have to subtract the two triangles A and B. A has height 1 and base x. B has base 1+x and is similar to A. From this we find that A has an area of (sqrt3-1)/2 and B has an area of 3(sqrt3-1)/2.

This means that the visible blue region is also 10 square units.

The horizontal component of the lower right side of the blue square is the same as the vertical component of the lower left side, so 2 units, so the overall rectangle has sides 5 and 6. Therefore the green region also has area of 10 square units.

The areas of the red, blue and green regions are all identical.