
What is the formula for the surface area of a box?
Answer
411k+ views
Hint: Here we have to find the formula for the surface area of a box. Firstly we will form the diagram of the box then we will level all the dimensions of it. As we know a box is either in the shape of a rectangle or a square so we will form a common formula to find the surface area by adding the area of each surface of the box and get our desired answer.
Complete step by step solution:
We have to find the formula for the surface area of a box:
Firstly we will form the diagram a box as follows:
Here we have taken
Height
Length
Width
Now as we can see that the box has six faces all are in rectangle shape.
The top and bottom face have sides as and …
The left and right faces have sides as and …
The front and back face have sides as and …
Next we know the rectangle area is calculated as follows:
Area
Where, are the two sides
For statement (1) we have area of two faces as:
Area …
For statement (2) we have area of two faces as:
Area …
For statement (3) we have area of two faces as:
Area ….
So we will get the surface area of box by adding equation (4), (5) and (6) as follows:
Surface Area of a box
Surface Area of a box
Hence formula for surface area of a box is .
Note:
Box is in the shape of a cuboid or a cube. That is the reason we have taken six sides of it and calculated the area of each side separately. Cuboid is a three-dimensional figure which is made up of six rectangular planes. We can see the common example of cuboid in a brick, pencil box etc. The opposite sides of a cuboid have the same dimension and are always parallel to each other.
Complete step by step solution:
We have to find the formula for the surface area of a box:
Firstly we will form the diagram a box as follows:

Here we have taken
Height
Length
Width
Now as we can see that the box has six faces all are in rectangle shape.
The top and bottom face have sides as
The left and right faces have sides as
The front and back face have sides as
Next we know the rectangle area is calculated as follows:
Area
Where,
For statement (1) we have area of two faces as:
Area
For statement (2) we have area of two faces as:
Area
For statement (3) we have area of two faces as:
Area
So we will get the surface area of box by adding equation (4), (5) and (6) as follows:
Surface Area of a box
Surface Area of a box
Hence formula for surface area of a box is
Note:
Box is in the shape of a cuboid or a cube. That is the reason we have taken six sides of it and calculated the area of each side separately. Cuboid is a three-dimensional figure which is made up of six rectangular planes. We can see the common example of cuboid in a brick, pencil box etc. The opposite sides of a cuboid have the same dimension and are always parallel to each other.
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