ABCD is a parallelogram.ADis producedtoE,AF=6 units,AF is parallel DC and the area of traiangle BCE is 33 units
Since AD is produced to E, we have a triangle AEF formed. Since AF is parallel to DC, angle AEF is equal to angle C.
Let x be the length of AF = 6 units.
Since ABCD is a parallelogram, triangles ADE and ABC are similar. Therefore, the ratio of the sides of ADE to ABC is the same as the ratio of the sides of AEF to BCF.
The ratio of the sides of AEF to BCF is x/BC.
Since the area of triangle BCE is 33 units, we have:
(1/2) x CE = 33
CE = 66.
Since CE is twice the length of BC, we have:
BC = 33.
Therefore, the length of AF (x) is 6 units and the length of BC is 33 units.