Question

The dimensions of a box are 1 m, 80 cm and 50 cm. Find the area of four walls.

Answer 1

Hint: In this question it is given that the dimensions of a box are 1 m, 80 cm and 50 cm. Then we have to find the area of four walls. So to understand it in better way we have to draw the diagram,

So to find the solution we need to know the total surface area of the above box (cuboid), if l, b and h be the length, breadth and height of the given cuboid then the total surface area (S) = 2 (lb + bh + hl).............(1)
Now in order to find the surface area of 4 walls we have to subtract the area of top and bottom from the total surface area (S).

Complete step-by-step solution:
Here, it is given, the length(l) of the box = 1 m = 100 cm.
Breath(b)= 80 cm and height(h)=50 cm.
Therefore,
By the formula(1), the total surface area(S)=2 (lb + bh + hl)
 =$$2\left( 100\times 80+80\times 50+50\times 100\right) \ cm^{2}$$
 =$$2\left( 800+400+500\right) \ cm^{2}$$
 =$$2\times 1700\ cm^{2}$$
 =$$3400\ cm^{2}$$
Now since we have to find the surface area of the four walls.
So for this we first need to find the area of the top and bottom surface and after that we have to subtract them from the total surface area (S).
The area of top surface ABCD=$$ l\times b$$=$$100\times 80\ cm^{2}$$=$$800\ cm^{2}$$
The dimensions of the bottom surface is same as the top surface, so we can say that the area if the bottom is also $$800\ cm^{2}$$
Therefore, the area of the top and bottom surface = $$2\times 800\ cm^{2} = 1600\ cm^{2}$$ .
$$\therefore$$ The area of the 4 walls = Total surface area(S) - Area of top and bottom
                                                     =$$3400\ cm^{2}-1600\ cm^{2}$$
                                                     =$$(3400-1600)\ cm^{2}$$
                                                     =$$1800\ cm^{2}$$
Which is our required solution.
Note: If you want to avoid the lengthy step then you can directly apply the formula for the surface area of four walls which is $$A=2\left( b+l\right) h$$.
Now you might be thinking that how we get this formula, so the concept is same as the solution that we have to subtract the surface area of the top and bottom of the above box, and from the diagram we can easily say that the area of the top and bottom is $$l\times b$$ now we have to subtract two times.
So therefore,
Area of four walls = Total surface area(S) - Area of top and bottom
                             =$$2\left( lb+bh+hl\right) -2\times lb$$
                             =$$2lb+2bh+2hl-2lb$$
                             =$$2bh+2hl$$
                             =$$2\left( b+l\right) h$$
This is how we get the surface area of the 4 walls.