Ok so to find the area of two sides (Length*Height)*2 sides, we are going to require to find the area of adjacent sides (Width*Height)*2 sides, so find the area of ends (Length*Width)*2 ends, Now it's time to integrate the three areas together in order to find the surface of the area. Okay so the surface area of a rectangular prism 5 cm long, 3 cm. wide and 2 cm. high = 5*2*2 + 3*2*2 + 5*3*2 = 20 + 12 + 30 = 62 cm2
Cube= 2ab+2bc+2ac
The area for top and bottom is (side lengths a and c) = a*c. So as we look at it there are at least two of them, so you'd get 2ac. Now for the front and back we have the side length of b and c, so the area of one of them is b*c, so as we look at it there are two of then. The surface area of those two is 2bc. Left and right sides have a side length of a and b, so of course the surface area of one of them is a*b. There are two of them, and from that their combined surface area is 2ab.