How to get the area of the trapezoid? I have the following basic geometry exercise, but I only know 3 sides. And I must not solve it with trigonometry.

Well, with trigonometry it is trivial. But with the formula of the trapeze area, I can not get the height.
So, How can I get the area? Thanks in advance.
 A: That the angle is 30° is the giveaway. If you drop the perpendicular of $C$ onto $AB$ so the foot is $E$, $\triangle CEB$ is half of an equilateral triangle. It follows that the height $CE$ is half of $CB$, or 6, and the whole area follows.
A: The area of a trapezoid is given by $$A=h\cdot\frac{a+c}{2}$$ where $h$ is the height, $a$ is the lower base, $c$ is the upper base. In your case this it's $a=|AB|,c=|CD|$. We have those lengths given, so all that remains is the height $h$. Now consider a line $l$ going through point $C$ perpendicular to $AB$, denote the intersection point of $l$ and $AB$ for example $X$ then $\Delta XBC$ is a triangle with right angle at $X$. The height of the trapezoid is then $|XC|=h$. By elementary trigonometry $$\sin{30°}=\frac{1}{2}$$ also  $$\sin{\alpha=\frac{\text{opposite}}{\text{hypotenuse}}}$$
which in this case is
$$\sin{30°}=\frac{|XC|}{|BC|}=\frac{h}{12}=\frac{1}{2}$$
from which you get that $h=6$ and so your area is then 
$$A=h\cdot\frac{a+c}{2}=6\cdot\frac{30+8}{2}=114$$
A: So start with drawing a perpendicular line on AB which connects point C, making that a new point on line AB called point "E". Do the same thing on the left side by making another point on line AB called the point "F". Now you have a rectangle proving DC : FE and DF : CE. Both sides measuring 8. If you subtract AB - FE and divide the answer with 2, you now have the the measure for AF : BE which is 11. As CB = 12 you can now use Pythagorean Theorem to get measures of  DF and CE.BC^2 - BE^2 = CE^2, the square root √(BC^2 - BE^2) = CE. √(12^2 - 11^2) = 4.795831523. 
Area of Trapezoid = ((30+8)÷2)4.795831523)
                                 = 91.12079894
