Trapezoid - Geometry - Area of a Trapezoid
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# Trapezoid

Trapezoid

A trapezoid is a kind of quadrilateral that has at least two sides that are parallel to each other. A parallelogram is a trapezoid that has two pairs of parallel sides, and a rhombus is a special kind of parallelogram, and so are rectangles and squares.

To figure out the perimeter of a trapezoid, you can add the lengths of all the sides together. To figure out the area of a trapezoid, you have to cut it into shapes that are easier to figure out. You want to cut it into a rectangle and two right triangles. Draw a line from one angle so that it is perpendicular to the opposite side, and another line from the opposite angle that is parallel to your first line, and also perpendicular to the opposite side. This will make a rectangle and two right triangles (one of them upside-down).

The area of the rectangle is the height multiplied by the width. The areas of the right triangles are the height multiplied by the width, divided by two. Add the areas of the triangles and the rectangle together, and you've got the area of your trapezoid.

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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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