Area of a Triangle - Geometry Made Easy

Area of a Triangle

To figure out the area of a triangle, multiply the base by the height of the triangle, and then divide by two: (Base x Height)/2. That's because the height times the base gives you the area of a quadrilateral, and in this case it's the area of the quadrilateral made by putting together two of your triangles. So when you divide it in half, you have the area of one triangle.

That's not hard if you have a right triangle, because one side is the base and the other side is the height. But what if your triangle has three sides that are all different lengths, and no right angles?

In that case, pick any side to be the base. Draw a line from the opposite angle down to your base, so that your line meets the base at a right angle, so it's perpendicular to the base. That's the height. Now measure the height and the base, multiply them together, and divide by two.

If you have a triangle with three sides of different lengths, and you don't know at least two of the lengths, then you can't figure out the area.

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Professor Carr

Karen Eva Carr, PhD.
Assoc. Professor Emerita, History
Portland State University

Professor Carr holds a B.A. with high honors from Cornell University in classics and archaeology, and her M.A. and PhD. from the University of Michigan in Classical Art and Archaeology. She has excavated in Scotland, Cyprus, Greece, Israel, and Tunisia, and she has been teaching history to university students for a very long time.

Professor Carr's PSU page

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