(1) Cross D to DE//AC to BC in E.

So the angle BDE=90 degrees, and the quadrilateral is a parallelogram.

So AD=CE

Because AD+BC=4 times the root number 2cm.

So BE=CE+BC=4 times the root number 2cm.

Because the quadrilateral ABCD is an isosceles trapezoid

So AC=BD=DE

Because in a right triangle, BD square +DE square =BE square.

So BD=AC=4.

② Because in triangle ABD and triangle CDE

AB=CD，AD=CE，BD=DE

So triangle ABD and triangle CDE are congruent.

So the areas of the two are equal.

So the area of trapezoidal ABCD is equal to the area of triangular BDE = 1/2*BD*DE=8.

In fact, it is very simple to accumulate more foundations and commonly used auxiliary lines.

For example, the translation diagonal of trapezoid, double height, translation waist

Come on! :)