How to Find the Area of a Triangle

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To find the area of a triangle, multiply half of the triangle’s base times its height. Mathematically, this procedure is described by the formula A = 1/2 x b x h, where A represents the area, b represents the base and h represents height. Specifically, the base is the horizontal length from one end of the bottom line of the triangle to the other edge. And the height -- also known as the altitude -- is the vertical length upward from the base to the corresponding vertex, or top-most point of the triangle.

Solved Example

To find the area of a triangle that has a base of 5 inches and a height of 4 inches, substitute 5 and 4 into the formula A = 1/2 x b x h, which yields A = 1/2 x 5 x 4. Multiply the first two numbers, giving A = 2.5 x 4. Finish the multiplication, which produces A = 10, and label the answer with the given units: 10 inches.

If You Don't Know the Height

In more advanced math classes, such as algebra, geometry or trigonometry, you might see math problems in which you don’t know the height of the triangle. If you do know the lengths of all three sides, however, you can use Heron’s formula. To use this formula, find the semi-perimeter, s, by adding the lengths of the three sides, which are usually denoted as a, b and c. Divide that total by two. Then, simplify s x (s – a) x (s – b) x (s – c), and take the square root of this result. If you know the lengths of two sides, which are usually labelled as a and b -- and the angle between them, C -- you can use the trigonometric formula A = 1/2 x a x b x sinC. Typically, you’ll see both of these formulas written with the multiplication symbols omitted -- that is, square root s(s – a)(s – b)(s – c) and A = 1/2absinC.


About the Author

Based in western New York, Amy Harris began writing for Demand Media and Great Lakes Brewing News in 2010. Harris holds a Bachelor of Science in Mathematics from Penn State University; she taught high school math for several years and has also worked in the field of instructional design.

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