Understanding the relationship between the perimeter and the area of a square is fundamental to many geometric calculations. In this article, we will explore how to calculate the area of a square when its perimeter is given.

What is the Area of a Square if Its Perimeter is Given?

Let's start with a step-by-step guide to find the area of a square given its perimeter.

Step 1: Calculate the Side Length

The perimeter (P) of a square can be calculated using the formula:

[ P 4s ]

where s is the length of one side. If the perimeter is given as 64 cm, we can use the formula to find the side length:

[ 64 4s ]

Dividing both sides by 4:

[ s frac{64}{4} 16 text{ cm} ]

Step 2: Calculate the Area

The area (A) of a square is given by the formula:

[ A s^2 ]

Substituting the side length found in the first step:

[ A 16^2 256 text{ cm}^2 ]

Other Approaches to Find the Area

Let's explore other scenarios where the perimeter is different but the method is similar.

Example 1: Perimeter is 72 cm

Using the same formula, we can calculate the side length and then the area:

[ 72 4s ]

Dividing both sides by 4:

[ s frac{72}{4} 18 text{ cm} ]

The area is:

[ A 18^2 324 text{ cm}^2 ]

Example 2: Perimeter is 4s 72 cm

Dividing both sides by 4:

[ s frac{72}{4} 18 text{ cm} ]

The area is:

[ A 18^2 324 text{ cm}^2 ]

Conclusion

By following these steps, you can easily calculate the area of a square when its perimeter is given. The key formulas to remember are:

Perimeter of a square:

[ P 4s ]

Area of a square:

[ A s^2 ]

Whether the perimeter is 64 cm or 72 cm, the method remains the same, ensuring consistency and accuracy in your calculations.