If I am understanding you correctly, first solve for the whole sector, which you can use this formula.
[tex] \frac{\Theta}{360} \pi r^2[/tex]
Once you find the area of the sector, all you have to do is get the area of the triangle and then subtract the area of the triangle from the sector and that will tell you the area of CFD and CED and let you know which one is greater.
For instance, Lets find A
sector area = [tex] \frac{90}{360} \pi 10^2 = 25\pi [/tex]
Now lets get the area of the triangle, which is
area triangle = [tex] \frac{1}{2} bh\sin C[/tex]
area triangle = [tex] \frac{1}{2} \times 10 \times 10 \times sin 90 = 50m^2[/tex]
CED = sector area - area of triangle = [tex] 25\pi - 50 = 28.53m^2[/tex]
Now lets find B
sector area = [tex] \frac{60}{360} \pi 12^2 = 24\pi [/tex]
Now lets get the area of the triangle, which is
area triangle = [tex] \frac{1}{2} bh\sin C[/tex]
area triangle = [tex] \frac{1}{2} \times 12 \times 12 \times \sin 60 = 36\sqrt(3)[/tex]
CFD = sector area - area of triangle = [tex] 24\pi - 36\sqrt(3) = 13.04m^2[/tex]
So A has the greater area base.
