Question

Find the area of the square of perimeter \[12\] cm?

Answer 1

Hint:In this question, we need to find the area of the square and also given that the perimeter of the square is \[12\] cm. First, we can find the side of the square with the help of the perimeter of the square given. We know that all the sides of the square are the same. The perimeter of the square is given by \[4a\] , where \[a\] is the side of the square. Then we can apply the formula for the area of the square to get the answer.

Formula used :
The perimeter of the square,
\[P = 4a\]
The area of the square,
\[A = a^{2}\]
Where \[a\] is the side of the square.


Complete step by step answer:

Given, the perimeter of the square is \[12\] cm.
Here we need to find the area of the square.
First we can find the side of the square \[(a)\] .
The formula for the perimeter of the square is \[4a\] and the given perimeter is \[12\] cm.
On equating both,
We get,
\[\Rightarrow \ 4a = 12\]
On dividing by \[4\] on both sides,
We get,
\[\Rightarrow \ a = \dfrac{12}{4}\]
On simplifying,
We get,
\[\Rightarrow \ a = 3\]
Thus we get the side of the square, \[a = 3\ cm\]
Now we can find the area of the square with side \[3\] cm .
We know that the formula for the area of the square ,
\[A = a^{2}\]
On substituting \[a\] ,
We get,
\[\Rightarrow \ A = \left( 3 \right)^{2}\]
On simplifying,
We get,
\[A = 9\]
Thus we get the area of the square is \[9\ cm^{2}\]
The area of the square is \[9\ cm^{2}\] .

Note:A square is nothing but a regular polygon with four equal sides. To calculate the area of a square, multiply its side to itself since all the sides of the square are the same . Also, we need to remember the formula of perimeter of the square then only the value of the side will be found . Sometimes we may make mistakes in perimeter and area i.e. instead of adding all the sides and finding the perimeter of the square, we may get confused with both the formulas.