Q:

# What is the formula for the area of a trapezoid?

A:

The area of any trapezoid with base side lengths "b1" and "b2" and height "h" is given by the formula A = h(b1 + b2)/2. The base sides are the trapezoid's two parallel sides. The trapezoid's height is the length of a perpendicular line drawn between the two base sides.

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The formula for the area of a trapezoid can be derived graphically. If any trapezoid is duplicated, this shape can be rotated 180 degrees and rearranged, along with the original trapezoid shape, into the shape of a parallelogram. If the original trapezoid has base side lengths b1 and b2 and a height h, the resultant parallelogram will have sides of length"b1 + b2 and height h. The area of a parallelogram is given by the formula A = base x height, so the newly generated parallelogram will have an area of A = (b1 + b2)h. Since this parallelogram is comprised of two trapezoids of equal area, the area of one of these trapezoids is just half that of the parallelogram, or A = h(b1 + b2)/2.

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