Concept Of Area
Area of a plane figure is the space enclosed by its perimeter. A good way to understand area is to look at painting a surface. Let's say you are trying to paint a plain sheet of paper. How much paint would it need? Of course you realise that it depends on the size of the paper. In other words area is measure of any particular surface.
By definition, a square whose sides are $1$ unit each, has an area of $1\ unit^2$ Here unit is the unit of length you have used to measure the sides of the square.
If you have chosen a square of sides $1$ cm each, then the area of the square is $1\ cm^2$
These are sometimes read (and written as) $cm\ square$ or $cm\ sq$ or $sq.\ cm$
If you have a square whose sides are $1$ inch, then the area of the square is $1\ inch^2$
How much is the are of a rectangle, as shown below, of length $8$ cm and width $5$ cm?
-----------book page break-----------
Lets divide the rectangle into smaller, square tiles of sides $1$ cm, like shown below :
As we saw before the area of each tile is $1\ cm^2$. How many tiles are there in all? There are $8$ columns each containing $5$ rows. So, there are $40$ tiles in all. Adding up the areas of all the smaller tiles, we get a total area of $40\ cm^2$.
So, we can see that the area of a rectangle is its length multiplied by its width.
Remember, it doesn't matter what unit you use to measure the sides, as long as both the length and the breadth are expressed using the same unit the value of the area will be length x breadth and the unit will be your chosen $unit^2$
For example the area of a rectangular tile of length $3\ ft$ and breadth $2\ ft$, will be $6\ ft^2$