Question

Perimeter of a square is $40cm$. Find the area of the square.

Answer 1

Hint: Perimeter of a square and area of a square depends on one value, that is the side of the square. So we can find the side of the square using the perimeter given and thus find the area. Perimeter is the sum of the sides of the square.

Formula used:
For a square of side a,
Perimeter of the square is the sum of all sides.
$ \Rightarrow Perimeter = 4a$
Also $Area = {a^2}$

Complete step-by-step answer:
The perimeter of the square is $40cm$.
We are asked to find the area.
For a square of side, a,

Perimeter of the square is the sum of all sides.
$ \Rightarrow Perimeter = 4a - - - (i)$
Also $Area = {a^2} - - - - - (ii)$
So, we have to find the side of the square using the equation $(i)$ and substitute it in equation $(ii)$ to find the area.
Substituting for perimeter in $(i)$ gives
$ \Rightarrow 40 = 4a$
Dividing both sides by $4$ we get,
$ \Rightarrow a = \dfrac{{40}}{4} = 10$
Therefore the side of the square is $10cm$.
Now substitute this value in $(ii)$ to find the area.
$ \Rightarrow Area = {a^2} = {10^2} = 100$
Hence the area of the square is $100c{m^2}$.

Additional information:
Since a square has equal sides, each side is one fourth of the perimeter. But in case of a rectangle the length and breadth is different. So it is not possible to find length and breadth using perimeter only.

Note: Alternatively if we were given area of the square, then we could find the perimeter as well. Or if the side of the square is given directly, then we can substitute it in equations to find either area or perimeter.