Using Surface Command to create a surface in the xy-plane

Question

Here is the figure I've sketched using GeoGebra.

I know already how to use the Surface Command to generate that surface in pink color. Specifically, it is given by

Surface(us(t)+(1-u)r(t),t,x(B_{2}),x(A_{2}),u,0,1)

where s(t) and r(t) are the parametric curves from A_{2} to B_{2} and from G to F, respectively.

May I know how to write the surface command for the surface determined by the four points that are plotted in the xy-plane as presented in the figure?

Answer 1

At last, I was able to provide the desired surface command. The command is given by Surface(tcos(v),tsin(v),0,t,a,b,v,arctan(m),arctan(n)) where

a=radius of the small circle

b=radius of the big circle

m=slope of the line that contains A_{1} and A_{2}

n=slope of the line that contains B_{1} and B_{2}.