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I have the diameter of an Isosceles trapezoid, and nothing else except the height. Is there any formula for finding the area of this shape with the given details? I've searched all over on Google, but couldn't find anything.

Abolfazl Malekpour
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The trapezoid is isosceles, so it looks like a rectangle with two congruent right triangles pasted on each end. Cut off one of those triangles and paste it on the other side to form a rectangle of the same area. Now you have the diagonal $d$ of the rectangle and its height $h$, so the area is

$$A = h\sqrt{d^2-h^2}.$$

B. Goddard
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