Limacon/Polar area?

Question

This question has bugged me for awhile. Find area inside the loop of the following limacon r= 5-10sin(theta). Please do not come up with 222.031538. I try and it's not correct. Anyone?

Answer 1

I was wrong
To correct
Area inner loop = 1/8*100(2pi-3sqrt3)
Area between loops = 1/8*100 (4pi+3sqrt3)
Sum of: area between loops + area inner loop = 1/8*100*6pi=
235.6194
This in the case b=a/2 (this case)