Find the height of a rectangular trapezoid if its large side is 10cm and the base difference is 8cm.

Suppose that in trapezoid ABCD, angle A is straight, then BC will be less than the base, and AD, on the contrary, is larger than the base. Draw a perpendicular from point C to side AD and mark it with point M.

And since the difference between the bases of the two bases is 8 centimeters, from here we conclude that MD = 8.

Now consider the triangular CMD.

CM² = CD² – MD²;

From which it follows that:

CM² = 10² – 8² = 36;

Therefore, 6 cm will be CM, which was required to be found in the conditions of the problem.

Answer: the height of the rectangular trapezoid is 6 centimeters.