Certainly! Let's go through the steps to solve this problem.
### Step 1: Understand the Problem
We are given a piece of wire that is 36 cm long. This wire is to be bent to form a perfect square. We need to find the area of the square formed by this wire.
### Step 2: Calculate the Side Length of the Square
To form a square using the wire, we need to know the length of each side of the square. The perimeter of a square is calculated by summing the lengths of all four sides.
Given the perimeter (P) of the square is 36 cm, we can use the formula for the perimeter of a square:
[tex]\[ P = 4 \times \text{side length} \][/tex]
We can solve for the side length (s) by rearranging the formula:
[tex]\[ \text{side length} = \frac{P}{4} \][/tex]
Substitute the given perimeter into the formula:
[tex]\[ \text{side length} = \frac{36 \, \text{cm}}{4} = 9 \, \text{cm} \][/tex]
### Step 3: Calculate the Area of the Square
Now that we know the side length of the square, we can find the area. The formula for the area (A) of a square is:
[tex]\[ A = \text{side length}^2 \][/tex]
Substitute the side length into the formula:
[tex]\[ A = (9 \, \text{cm})^2 = 81 \, \text{cm}^2 \][/tex]
### Conclusion
The area of the square formed by folding the 36 cm wire is [tex]\( 81 \, \text{cm}^2 \)[/tex].
