Question

Using algebraic expressions, calculate the surface area of the four walls of a room. What happens when you include the floor ? What if you add the ceiling too?

Answer 1

Suppose l, b and h be the length, breadth and height of each of four walls of a room.
There are 2 pairs of walls corresponding to length and breadth each.
One of the pair is $l\times h$ and other pair is $b\times h$ .
So the surface area of both pairs of walls = $2\left(l\times h+b\times h\right)=2h\left(l+b\right)$
Therefore, surface area of four walls = $2h\left(l+b\right)$
When we include the floor, this means surface area of floor is also added.
And the surface area of floor = $l\times b$
Then surface area of four walls including floor = $2h\left(l+b\right)$ + $l\times b$
Also, surface area of ceiling = $l\times b$
Similarly, when we include the ceiling, then surface area of ceiling is also added.
Then, Total surface area of room = $2h\left(l+b\right)+lb+lb=2lh+2bh+2lb=2\left(lb+bh+lh\right)$