Question

A square carrom board has a perimeter of 320cm. How much is its area?

Answer 1

Hint: For solving this question you should know about the perimeter of a square. The perimeter of a square is the sum of all the sides or multiplying one side by 4. In this problem we will calculate one side from the given perimeter and then we will find the area of this square with the help of the formula.

Complete step by step solution:
According to our question, it is asked to us to find the area of a square and the perimeter of that square is already given. As we know that a square is a shape covered with four sides and each side is at ${{90}^{\circ }}$ angle with each other. And the main quality of the square is that it has all sides as equal. The preference of a square is the sum of all four sides or as we know that all sides are equal, so we can simply multiply a single side with 4 and we can get the perimeter of a square. So, if we see an example for this, then here is a square of side $a$.

So, the perimeter of this is $4a$ and the area is ${{a}^{2}}$.
So, according to our question,
Perimeter of the square = $320cm$
Consider the side as $a$, then,
$\begin{align}
  & 4a=320 \\
 & \Rightarrow a=\dfrac{320}{4}=80cm \\
\end{align}$
Now,
Area of a square $={{a}^{2}}$
Area of this square $={{\left( 80 \right)}^{2}}=80\times 80$
Area of the square $=6400c{{m}^{2}}$
So, the area of this square is $6400c{{m}^{2}}$.

Note: While solving this type of question you have to be sure about the square shape and the rectangle shape because both are the same in angles but the four sides are equal in square and only opposite sides are equal in a rectangle. So, the perimeter of both are also different due to this.