Any room that is in the shape of a cuboid has four walls excluding the floor and the ceiling. By the area of four walls, we mean the total area of these four walls each of which are rectangles.
Suppose that the room has length l, breadth b, and height h. Then the formula for the area of the four walls of the room is given as,
Area of Four Walls = 2(l+b)h
Notice that this formula is different from the formula for the total surface area of the cuboid. This is because the total surface area includes the area of the floor and the ceiling as well.
We now give some examples where the formula for the area of four walls can be used. We also explain how we can derive the formula for the area of four walls.
Example 1:
Suppose that a room has a length of 13m, a breadth of 12m, and a height equal to 10m. Calculate the area of the four walls of the room.
Solution: Given, l = 13m, b = 12m, and h = 10m.
Applying the above formula we have that,
Area of Four Walls = 2(l+b)h = 2 x (12 + 13) x 10 = 2 x 15 x 10 = 300m2 or 300 sq. meter.
Note that even though the lengths are given in meter units, the area is given in the m2 or 300 sq. meter units.
Example 2:
The area of the four walls of a room is 144 m square. if the length of the room is thrice the breadth and the height is 3 m. find the area of the floor?
Solution: Given, A = 144 cm square, and h = 3m.
Let us assume that the breadth of the room is equal to x. So, b = x.
Since the length is thrice of the breadth of the room we have that,
l = 3 x b = 3x
Applying the four walls formula we have that,
Area of Four Walls = 2(l+b)h
144 = 2 x (3x + 3x) x 3
144 = 2 x 3x x 3 = 18x
18x = 144 implies x = 144/18 = 8m
Now since x= 8m, we have that,
Breadth = 8m and, Length = 3x = 24m
So, Area of Floor = Length x Breadth = 8 x 24 = 192 m2.
How do we Derive the Area of Four Walls Formula:
The total area of the four walls is found by adding the area of each of the four rectangular walls excluding the floor and ceiling of the room. We find the area of the rectangle by multiplying the length and the breadth and then add up the resulting areas.
Area of first wall = l x h = lh
Area of second wall = l x h = lh
Area of third wall = b x h = bh
Area of fourth wall = b x h = bh
Total area = lh +lh +bh + bh = 2lh + 2bh = 2(lh + bh) = 2(l+b)h
Conclusion:
