Question

How do you find the area of a square with sides $6$ centimeters long?

Answer 1

Hint: Let us assume that the length of the given square is $6$ cm. Let this be equation (1). We very well know that if the length of the side of a square is equal to $x$ cm, then the area of the square is equal to $x^2$ sq.cm. Let us say that the area of the square is equal to $A$ sq.cm. So, we are now supposed to find the square of value of $x$ cm which is obtained from equation (1). Let this be equation (2). Now, from equation (2) we can easily find the value of the area of the square whose sides are $6$ cm long.

Complete step-by-step answer:
Before solving the given question, we should keep in mind that if the length of the side of a square is equal to $x$ cm, then the area of the square is equal to $x^2$ sq.cm.
It is already given that the length of the side of the square is equal to 6 cm. Let us assume that the side of the square is equal to $x$ .
 $\Rightarrow x=6$ ---(1)
We already know that the area of the square with side $x$ cm is equal to $x^2$ sq.cm.
 $\Rightarrow A=x^2$ --(2)
Now, we substitute equation (1) in equation (2). After doing so, we get,
 $$\begin{gathered} \Rightarrow A={\left(6\right)}^2 \\ \Rightarrow A=36 \end{gathered}$$
So, it is clear that the area of the square whose side is equal to $6$ cm is $36$ sq.cm.
Thus, Area = $36c{m}^2$ .
So, the correct answer is “Area = $36c{m}^2$ ”.

Note: There is usually a misconception among students, which is that if the diagonal of a square is equal to $x$ cm, then the area of the square is equal to $x^2$ sq.cm. Due to this misconception the answer gets affected. Thus, this misconception should be avoided.