What is the area of the trapezoid shown? Express your answer in simplest exact form.

I know that the base is 4 but I don't know the height.

Your base is correct !!!!

Draw a an altitude from the top right vertex to the base

This forms a 30-60-90 right triangle......which has sides of 1 , sqrt 3 and 2

sqrt 3 is the altitude (height)

Can you take it from there ???

Thank you!