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Formulas are often times thought of as special types of equations where two or more quantities are equated to one another.
There are several different types of formulas that we will come across when working in most math courses. Here are a few of the most common formulas.
The area of a rectangle is equivalent to multiplying the length and width of the rectangle together.
The area of a triangle is equivalent to the base times height, divided by 2, or multiplied by one-half.
The area of a circle is equivalent to pi times the radius squared.
The volume of a rectangular prism is equivalent to the length times the width times the height of the prism.
The volume of a right cylinder is equivalent to pi times the radius squared times the height.
The formula for the volume of a sphere, which is equivalent to four-thirds times pi times the radius cubed, or .
Formulas become most handy when we are given the value of several quantities and asked to determine the value of another quantity. For example, suppose we are told that a rectangle has an area of 40 square feet and a base of 4 feet. What would the height of the rectangle be?
To calculate the length of the rectangle, we can take the area, A, and base, b, and substitute them in the formula for a rectangle’s area. We can then solve for the height, h.
Area of a Rectangle Formula | |
Substitute known values: , | |
Divide both sides by 4 ft | |
Our solution |
When we wish to tell whether or not we can use a formula in this way, we simply need to check that we have a value of all but one variable in the formula. If that is the case then we can solve for the unknown quantity using the appropriate formula.
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