Calculating the perimeter and area of geometric shapes like circles and squares is a skill you can use throughout your life. It comes in handy every time you build something, arrange something, or just try to figure out if one object will fit inside or alongside another. Often, it's much easier to measure perimeter than area of real-world objects. Once you know a couple of simple formulas, you can easily convert that perimeter to area using basic calculations.
TL;DR (Too Long; Didn't Read)
The formula for area of a square is (P/4)2, where P is the perimeter.
The formula for area of a circle is C2/4π, where C is the circumference (a special word for the perimeter of round or ovoid objects).
Calculating the Area of a Square
A square is the easiest shape for calculating area based on perimeter, between each of its sides is 1/4 the length of the perimeter. If you want your answer to be in terms of square feet, make sure your measurements are either in feet or converted into feet before you begin the calculations.
Divide the Perimeter by 4
Square the Length of One Side
Calculate the length of one side of the square by dividing the perimeter by 4. So if the perimeter of the square is 32 feet, you have:
32 ft ÷ 4 = 8 ft
Note that you carry the unit of measure – feet – along throughout your calculations.
Compute the area of the square by multiplying the length of one side by itself. So you have:
8 ft × 8 ft = 64 ft2
Calculating the Area of a Circle
You can also calculate the area of a circle based on its perimeter. As always, if you want your result to be in square feet, you must first ensure that all your measurements are in feet.
The perimeter of a circle is usually referred to as its circumference. The two different words mean exactly the same thing – the distance all the way around the outside of the figure – but circumference refers only to round or ovoid objects, while perimeter can refer to any two-dimensional shape.
Square the Circumference
Divide by 4 × Pi
The symbol π represents a constant number that mathematicians are still calculating. So far, they've found more than a quadrillion digits to the right of the decimal point. Obviously all those digits won't fit on your page or screen, so most teachers will let you abbreviate π as the value 3.14.
Square the circumference of the circle or, to put it another way, multiply the circumference by itself. So if the circumference of your circle is 10 feet, you'd have:
10 ft × 10 ft = 100 ft2
Again, note how you carry the units of measure through the calculations. But even though the result of this step is in square feet, you're not done finding the area of your circle yet. You still need to finish the rest of the formula.
Divide the result from Step 1 by 4π. The result is the area of the circle in square feet. This gives you:
100 ft2 ÷ 4(3.14) = 7.96 ft2