5.2.4.34 Various problems on the plane

Condition: In the trapezoid \( A B C D \) the base \( A D \) is greater than the base \( B C \). It is known that \( A D=C D= \) \( =14 / 3, \quad \angle B A D=\pi / 2, \quad \angle B C D=5 \pi / 6 . \quad \mathrm{Ha} \) on the basis of \( A D \) a triangle \( A E D \) is constructed. The points \( B \) and \( E \) lie on the same side of \( A D \) and \( A E=E D \). The length of the height dropped from the point \( E \) to the line \( A D \) is equal to \( 7 / 5 \). Find the area of ​​the common part of the trapezoid \( A B C D \) and the triangle \( A E D \).