I believe she would need to stain 548 inches of the surface.
Excluding the top and bottom, you are left with two panels that are 10 by 7.4, and two panels that are10 by 20, so
10•7.4= 74•2 =148
10•20= 200•2 =400
148 + 400= 548
Please correct me if I am wrong, have a good day!