Table of Contents |
When we try to determine how much space is covered in a two-dimensional space, we need to use the concept of area. For example, when buying a house we oftentimes will consider the total living space in a house, which is considering how much floor space the house has.
Because area is represented in two dimensions, we represent quantities of area as squared units. For example, we might say that a square living room has a total area of 625 square feet, which might mean that the length of the room is 25 feet and the width is 25 feet.
When calculating areas, there are a few common shapes that you will always come across, as we have previously defined. These shapes and their area formulas are listed below.
Let’s look at how we can use these different area formulas to find some unknown quantity.
EXAMPLE
Suppose we are told that a rectangle has a length of 10 feet and a width of 12 feet. How would we find the rectangle’s area?Multiply length by width | |
Units of feet are also multiplied | |
Our Solution |
Notice that when calculating area, we square the units of distance.
EXAMPLE
Suppose we are asked to find the area of a circle with a diameter of 9 inches. How would we make this calculation? As with the previous example, we start by writing down the appropriate area formula, and substitute in the quantities we know.Substitute 4.5 in for r | |
Square the radius | |
Our Solution, rounded to the tenths place |
Sometimes, we may be given the area of an object and need to back-solve to find the measurements of a given part of an object. Let’s look at some examples.
EXAMPLE
If the area of a square is 400 square feet what is the length of the square?Take the square root of both sides | |
Our Solution |
EXAMPLE
If the area of a circle is what is the radius of the circle?Divide both sides by | |
Take the square root of both sides | |
Our Solution |
Source: ADAPTED FROM "BEGINNING AND INTERMEDIATE ALGEBRA" BY TYLER WALLACE, AN OPEN SOURCE TEXTBOOK AVAILABLE AT www.wallace.ccfaculty.org/book/book.html. License: Creative Commons Attribution 3.0 Unported License