Perimeter 596m Square Area Calculation

The question asks us to determine the area of a square given its perimeter is $596$ m. The area needs to be expressed in square meters (m$^2$).

Understanding Square Geometry

To solve this, we first recall the properties and formulas related to a square:

• A square has four equal sides. Let's denote the length of a side by '$s$'.
• The perimeter ($P$) of a square is the total length around its boundary. The formula is $P = 4 \times s$.
• The area ($A$) of a square is the space it occupies. The formula is $A = s \times s$, or $A = s^2$.

Calculating the Square's Area Step-by-Step

We can find the area by following these steps:

1. Determine the side length ('s'):

   We are given the perimeter $P = 596$ m. Using the perimeter formula $P = 4s$, we can isolate '$s$':

   $ 596 \, \text{m} = 4s $

   To find the side length, we divide the perimeter by 4:

   $ s = \frac{P}{4} $

   $ s = \frac{596 \, \text{m}}{4} $

   Performing the division:

   $ s = 149 \, \text{m} $

   So, the length of each side of the square is $149$ m.

2. Calculate the area ('A'):

   Now that we have the side length ($s = 149$ m), we can use the area formula $A = s^2$:

   $ A = (149 \, \text{m})^2 $

   $ A = 149 \, \text{m} \times 149 \, \text{m} $

   Calculating the square of 149:

   $ A = 22,201 \, \text{m}^2 $

Final Area Result

The calculated area of the square is $22,201$ m$^2$. This matches one of the options provided.