How to Find the Area of a Triangle

Finding the area of a triangle generally involves a simple multiplication problem.
••• NUMAX3D/iStock/Getty Images

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.

Related Articles

How to Find the Long Side Dimension on a Right Triangle
How to Find the Missing Slope of a Trapezoid
How to Calculate Diagonal Distance Between Corners...
How to Write Equations of the Altitudes of Triangles
How to Split a Triangle Into Fourths
How to Find the Area of a Trapezoid Without the Length...
How to Calculate Triangles
How to Find the Radius of an Ellipse
How to Calculate Angles Without a Protractor
How to Solve Equations on Isosceles Triangles
Endpoint Math Formula
How to Identify a Trapezoid
How to Solve a Hexagon
How to Calculate the Area of Trapezoids
How to Calculate the Diagonal of a Triangle
How to Calculate the Volume of a Triangle
How to Find the Area & Width of a Rectangle
How to Calculate Sides of a Triangle
How to Solve for Both X & Y
How to Find One Side of an Isosceles Triangle

Dont Go!

We Have More Great Sciencing Articles!