If we let the dimensions of the rectangle be 2x and 2/x, then whatever the value of x, its area will be 4.

This means that the radii of the three semicircles will be:

x, 1/x and (x+1/x)

The area of a semicircle is (pi*r^2)/2, and we want the area of the larger semicircle, less the area of the smaller two. For simplicity we can take out the pi/2:

Area = pi/2 * ((x+1/x)^2 – x^2 – 1/x^2)

Area = pi/2 * (x^2 + 2(x/x) + 1/x^2 – x^2 – 1/x^2)

x gets cancelled out

Area = pi/2 * (2)

Area = pi

And that’s the answer!