Area of base times height=volume.
So area=vol/height=(8x^3+14x^2+x-2)/(2x+1)=4x^2+5x-2, option A.
(Quick tip: put x=1. Volume becomes 21, height=3, 21/3=7=4+5-2=area. None of the other options gives an area of 7. Also works putting x=0: -2/1=-2. Option A only fits.)