Drop a perpendicular from the top left corner to the bottom. Use sine of 30o (or cosine of 60o) to determine the length of the base of the triangle that you formed. It'll be the same when you do it to the right hand side. Add up all the lengths.
+54 Like what guest had said, drop two perpendicular heights from the left and right to the bottom of the trapezoid. Now, we have two 30-60-90 triangles and using those properties, the angle opposite to 90 degrees is two, so the angle opposite to 30 degrees is 1. Adding up all the side lengths, the perimeter is thus \(2+2+2+1+2+1=2(4)+2=\boxed{10}.\)
