Which Is Greater?

Adding a line to this image makes it easier to see its parts.

The two red parts combine to make a semi-circle with a radius of 2 and an area of $\frac{1}{2}\pi(2)^2 = 2\pi.$

The area of the entire figure is the area of a semi-circle with a radius of 3 minus the area of a semi-circle with a radius of 1: $\frac{1}{2}\pi(3)^2 - \frac{1}{2}\pi(1)^2 = 4 \pi.$

If the area of the figure is $4\pi,$ and the area of the region shaded red is $2\pi,$ then the area of the region shaded blue must also be $2\pi.$ The areas of the red and blue regions are equal.