What is the surface of a room a by b by c?

Answer 1

Presuming that a room is a rectangular prism, with a solid floor, ceiling and walls, we have 6 rectangles which make up the surface area of the room.

Since rectangular prism's are symmetrical, each side of the prism is identical to it's opposing side. Or in other words, if we say that the length of the floor is 'a', and the width of the floor is 'b', then the area of the floor is a * b, and the area of the ceiling is a * b. Thus we have that the surface area of the floor and ceiling combined is:

2 * a * b

Next, notice that all 4 walls have the same height. Also notice that 2 of the walls run along the length of the floor, and the other 2 walls run along the width of the floor. If we say that the height of the walls is 'c', then we have that the surface area of the walls that run along the length of the floor is:

2 * a * c

and the surface area of the walls that run along the width of the floor is:

2 * b * c

If we add all of these together, then we have that the total surface area of the room is:

2 * a * b + 2 * a * c + 2 * b * c

=

2 * (a*b + a*c + b*c)