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,
 $
   \Rightarrow A = {\left( 6 \right)^2} \\
   \Rightarrow A = 36 \;
  $
So, it is clear that the area of the square whose side is equal to $ 6 $ cm is $ 36 $ sq.cm.
Thus, Area = $ 36\;c{m^2} $ .
So, the correct answer is “Area = $ 36\;c{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.