In geometry, the trapezoid tends to be one of the trickier quadrilaterals to deal with because the opposite sides are not parallel. The top and bottom sides are parallel to each other, but the two slopes can be slanted toward or away from each other. The trick to calculating the dimensions of a trapezoid is to restate the problem in terms of a simpler shape, usually a right triangle. From this rearrangement, you can use simple calculations such as the Pythagorean theorem to determine the polygon's dimensions.
Recast the problem by creating a right-angle triangle with the missing slope forming the hypotenuse.
Determine the length of the base of this triangle by subtracting the measure of the lesser parallel side from the length of the longer parallel side.
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Insert, as the height of the triangle, the height of the trapezoid. Now you have a right triangle with known legs and an unknown hypotenuse.
Square the length of the two sides and add them together. For example, if the two sides are three and four inches long, square three (nine) and four (16) and add the products (25).
Take the square root of the resulting figure. If that result is 25, for example, the square root would be five. That number is the length of the missing slope of the trapezoid.