5.2.4.34 Various Problems on the Plane

Condition: in the trapezoid \ (a b c d \) the base \ (a d \) is more 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 {ha} \) the base \ (a d \) a triangle \ (a e d \) is built. The points \ (b \) and \ (e \) are on one side from \ (a d \) and \ (a e = e d \). The length of the height lowered from the point \ (e \) to the line \ (a d \) is equal to \ (7 /5 \). Find the area of the general part of the trapezoid \ (a b c d \) and a triangle \ (a e d \).