If you've ever measured the length, width or height of something, you've measured in a single dimension. Once you combine any two of those dimensions, you're talking about a concept called area – or how much space a shape takes up in two-dimensional space. Exactly calculating the area of wildly irregular shapes can require advanced math techniques like calculus. But for more common geometric shapes like circles, rectangles and triangles, you can find the area with a few simple formulas.
Before you start calculating area, take note: Every measurement must be done in the same unit of measure. So if you're calculating area in square feet, all measurements involved must be given in feet. If you're calculating area in square inches, all measurements must be given in inches, and so on.
Square Feet Formula for Rectangles and Squares
If the shape you're considering is a square or a rectangle, finding the area is as simple as multiplying length times width. When done in terms of feet, this formula comes in handy for everything from gauging the area of a lawn to calculating how big the rooms are in your house.
Formula: length × width
Example: Imagine you've been asked to calculate the area of a rectangular room that measures 10 feet by 11 feet. Plugging those dimensions into the formula, you have:
10 ft × 11 ft = 110 ft2
If you're calculating the area of a rectangle, you must use this formula. If you're calculating the area of a square, you have two choices: Either use this formula, or use your knowledge that all four sides of a square are equal length to develop an even simpler formula:
Area of square = length2, where length is the length of any single side of the square.
Calculating Square Feet of a Parallelogram
No need to plug the dimensions of a parallelogram into a square feet area calculator; you can calculate the area yourself by multiplying the parallelogram's base times its height.
Formula: base × height
Example: What is the area of a parallelogram with base 6 feet and height 2 feet? Substituting the data into the formula gives you:
6 ft × 2 ft = 12 ft2
Finding the Area of a Triangle
There's a square feet formula for triangles, too, and it's just one step more than finding the area of a parallelogram.
Formula: (1/2)(base × height)
Example: Imagine that you're faced with a triangle that has a base of 3 feet and a height of 6 feet. What is its area? Applying that information to the formula gives you:
(1/2)(3 ft × 6 ft) = 9 ft2
Calculating Area of a Circle
What if you're faced with a circle? Although you only need one measurement – the square's radius, usually denoted as r – there's still a formula you can use to find the circle's area.
The special number pi, usually written with the symbol π, is almost always abbreviated as 3.14.
Example: Imagine you've been asked to cut a circle out of cardboard with radius 2 feet. What will be the area of the finished circle? Substitute the information into your formula and you have:
πr2 = π(2 ft)2= π(4 ft2)
Most teachers will want you to substitute in the usual value of pi (3.14), which in turn gives you:
3.14(4 ft2) = 12.56 ft2
So the area of your circle is 12.56 feet squared.
- pattern shapes image by Leslie Batchelder from Fotolia.com