we know that
surface area of rectangular cake=area of the base+perimeter of base*height
only the top area is considered for frosting
area of the base=20*12----> 240 in²
perimeter of the base=2*[20+12]----> 64 in
height=6 in
surface area of rectangular cake=240+64*6----> 624 in²
the answer is
624 in²