Introduction to the Problem
Suppose you have a piece of wire that is 12 cm long. The challenge is to determine the area enclosed by forming a square with this wire. This article delves into the mathematical steps to find the solution and provides a comprehensive explanation suitable for SEO and Google's guidelines.
Understanding the Problem
The wire is bent to form a square, and the perimeter of the square is equal to the length of the wire. Therefore, the perimeter of the square is 12 cm.
Step-by-Step Solution
The first step is to find the length of one side of the square. Since a square has four equal sides, we divide the perimeter by 4:
Side Perimeter / 4
Side 12 cm / 4
Side 3 cm
Calculating the Area
The area of a square can be calculated using the formula:
Area Side^2
Substituting the value of the side:
Area 3 cm × 3 cm 9 cm^2
Verification and Confirmation
To ensure our solution is correct, let's verify the calculations:
The perimeter of the square is 12 cm. The side of the square is 3 cm. The area of the square is 9 sq cm.Common Mistakes and Clarifications
Some readers might make the following mistakes:
Forgetting to divide the perimeter by 4 to get the side length. Misunderstanding the formula for the area of a square (Area Side^2).It is crucial to pay attention to these details to avoid errors in your calculations.
Conclusion
In summary, a 12 cm wire can be bent to form a square with an area of 9 cm^2. This solution illustrates the importance of understanding basic geometric formulas and the step-by-step process in solving such problems.
Frequently Asked Questions (FAQ)
Q: If the wire is not very thin, does it affect the solution?
A: The thickness of the wire does not affect the calculation of the perimeter and the area of the square. The solution remains valid as long as the wire is rigid enough to form a square.
Q: How can I apply this to other shapes?
A: This method can be adapted to other shapes. For example, if the wire is bent into a rectangle with a given perimeter, you can use the perimeter to find the dimensions of the rectangle and then calculate its area.
Q: Are there other ways to solve this problem?
A: Yes, there are alternative methods. You can directly apply the formula for the area of a square if you know the side length, which is derived from the perimeter. Additionally, you can use the properties of the square, such as the fact that all sides are equal, to simplify the calculations.