I have this really hard question which is attached at the bottom. I am not supposed to use a calculator to solve it but I've been trying a few methods to work it out, and nothing has come nearer than calculus. I used the equation of a circle graph with radius 2 and found the integral from R to P, and multiplied it by 2.

However, I haven't actually technically 'learnt' calculus so I had to solve it with my calculator and got this:

Area from P to R =

Some devilish answer... and then there's all the tricky math involved in evaluating it. Anyways, after running it through the calculator and multiplying by 2 I get

__(B).__
Is there any simple (non-calculus?) way to solve this? It was a question on a very time-limited test. Thanks.