Answer
$96 \sqrt 3 \ mm^2$
Work Step by Step
The area of a trapezoid is equal to half the product of the sum of the bases and the height.
Suppose $a$ and $b$ are bases and $h$ is the height of a trapezoid.
The height of a trapezoid can be computed by the tangent ratio and the right triangle.
$tan 60^{\circ} =\dfrac{h}{6} \implies \sqrt 3 =\dfrac{h}{6}$
or, $h=6 \sqrt 3 mm^2$
Now, the area of a trapezoid $A=\dfrac{1}{2} (a+c)(h)\\=\dfrac{1}{2} (6+15+11)(6 \sqrt 3)\\= 96 \sqrt 3 \ mm^2$
