Area of a Triangle - Geometry Made Easy
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Area of a Triangle

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.

Triangles
Angles
Circles
More about Geometry

Bibliography and further reading about geometry:

More about Geometry
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Karen Carr is Associate Professor Emerita, Department of History, Portland State University. She holds a doctorate in Classical Art and Archaeology from the University of Michigan. Follow her on Instagram or Twitter, or buy her book, Vandals to Visigoths.
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