Question

The figure below shows AB = 4 units and BD = 6 units.

Triangle ADE has a point B on AD and a point C on AE. Segment BC is drawn parallel to side DE. AB measures 4 units and BD measures 6 units.

If the area of triangle ADE is 50 square units, what is the area of the trapezoid BCED?

Answer 1

Use similarity here: As the lines BC and DE are parrallel both the angles are similar by Angle-Angle-Angle criterion of similarity.

Now we are given that AB=4 and BD= 6
So AD=10

Now let us use some similarity rules for finding area.
This says that
Area1/Area2 = (Side1)^2/(Side2)^2
Side1/Side2 in the triangles ABC ~ ADE are
4/10
And we are given that Area of ADE = 50 square units.
So
ar(ABC)/50 = (4/10)^2 = 16/100
So area of triangle ABC = 8 Square units..
Now area of the trapezium = Area of Big Traingle - Area of small triangle = 50-8
Understood? :)