How to Calculate the Area of a Square Given Its Perimeter: A Detailed Guide
How to Calculate the Area of a Square Given Its Perimeter: A Detailed Guide
Understanding the relationship between the perimeter and area of a square is fundamental in geometry. If you know the perimeter of a square, you can easily determine its area. This article will guide you through the process step-by-step, providing detailed calculations and explanations.
Step-by-Step Calculation
Given the perimeter of a square is 72 inches, let's go through the process to find its area.
1. Calculate the Side Length
The perimeter of a square is the sum of all its sides. The formula for the perimeter is:
Perimeter (P) 4 × side (s)
In this case, we are given the perimeter (P) as 72 inches. We can set up the equation and solve for the side length (s):
72 4 × s
Divide both sides by 4:
s 72 ÷ 4 18 inches
2. Calculate the Area
The area of a square is the product of its side length squared. The formula for the area is:
Area (A) side length (s)2
Substitute the side length into the equation:
A 182 324 square inches
Additional Calculations
Calculation 1:
Perimeter of square 4 × side
72 4 × side
side 72 ÷ 4 18 inches
Area of square side × side 18 × 18 324 square inches.
Calculation 2:
Perimeter of the square 72 cm
So one side a 72 ÷ 4 cm
18 cm
Therefore, area of the square a2
182 sq. cm
324 sq. cm
Conclusion
Knowing that the perimeter of a square is 72 inches, we can confidently calculate that its area is 324 square inches. This method can be applied to any square, as long as you know its perimeter. Understanding these basic geometric principles will help you solve more complex problems in geometry and beyond.