That depends on what information that you do know. If you have length of a leg (I'm not sure if that is the correct term or not) and distance from that leg's vertex to a point directly below the other 'vertex', then you have a little right triangle and can use the Pythagorean Theorem (a2 + b2 = c2), where c is the longest side. So in this case you know b and c, so a2 = c2 - b2.
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Without the area or any other given measurements, it is not possible to determine the exact height of a trapezoid. The height of a trapezoid is a crucial measurement needed to calculate its area. Therefore, without this information, the height cannot be determined accurately.
Area of a trapezoid: 0.5*(sum of its parallel sides)*height
Area of a trapezoid = 0.5*(sum of parallel sides)*height
For a parallelogram, take the base times the height. For a trapezoid, take the smaller base and times it by the height.
Area of a trapezoid: 0.5*(sum of parallel sides)*height
A trapezoid is a polygon. Therefore, a trapezoid has no height