Calculating Square Area from Perimeter

This problem asks us to find the area of a square when we know its perimeter. Let's break down how to solve this step-by-step.

Understanding Square Properties

A square is a special shape with four equal sides. The perimeter is the total distance around the outside of the square. The area is the space enclosed within the square.

Step 1: Finding the Side Length

We are given that the perimeter of the square is 76 meters. The formula for the perimeter ($P$) of a square with side length ($s$) is:

$P = 4s$

To find the length of one side ($s$), we can rearrange the formula:

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

Now, we substitute the given perimeter value:

$s = \frac{76 \text{ m}}{4}$

Calculating this gives us:

$s = 19 \text{ m}$

So, each side of the square is 19 meters long.

Step 2: Calculating the Area

The formula for the area ($A$) of a square is the side length multiplied by itself:

$A = s \times s = s^2$

Using the side length we just found ($s = 19$ m):

$A = (19 \text{ m})^2$

$A = 19 \times 19 \text{ m}^2$

Calculating the square of 19:

$A = 361 \text{ m}^2$

Therefore, the area of the square is 361 square meters.

Final Answer

The area of the square is 361 $m^2$. This matches option 3.