# Calculate area of trapezoid with special triangles

the parallel sides of a trapezoid have lengths 7 cm and 15 cm. The two lower base angles are 30 and 60 degrees. The area of the trapezoid is..?

Two 30-60-90 degree triangles form on each side of the trapezoid. If I determine the height of one triangle, I can easily calculate the area of the two triangles and rectangle. But to obtain the height I must first obtain another side length. So my question is: how do I obtain a side length of any one of the triangles? Note that in the image, both triangles seem identical. I put it there for a little reference, while the real measurements/angles are based off the question.

Hint. If the base angles are $30^\circ$ and $60^\circ$, then the trapezium can be visualised as a $30$–$60$–$90$ triangle with (horizontally placed) hypotenuse $15$, minus a similar triangle with hypotenuse $7$.
Hint: Note that $h\cot (30^\circ)+h\cot(60^\circ)$ is equal to the difference $15-7$ of the parallel side lengths.