Triangle Prob: Given ACD, let F be the midpoint of....

[Fouad1013]

Please help me with this triangle problem.

Given triangle ACD as displayed below, let F be the midpoint of AE. Also, |AE| = (1/2)|ED|, |AD| = 18, |AB| = 9, and |BC| = 3.

      A *.
       /  \. F
      /     *\. E
     /         *\.
  B *             \.
   /                \.
C *-------------------* D

If the area of BEDC is 72 square units, find the area of the triangle BFE.

 

[merlin2007]

Re: Triangle Problem

The ratio of the area of triangle ABE to the area of the triangle ACD is (9*6)/(12*18).
This relation can be derived from the fact that Area = b*c*sin(A), in a triangle with sides a, b, c with vertices A, B, C opposite them.

Let the area triangle ABE be x. Then x / (x+72) = 54/516 = 1/4. Solving gives us x = 24.
Since the area of BFE is (1/2)(area of ABE), (same height, 1/2 the base), the area of BFE is (1/2)(24) = 12.

 

[Fouad1013]

I didnt take this area "Area = b*c*sin(A), in a triangle with sides a, b, c with vertices A, B, C opposite them" formula yet so i cant use it to find the area. My teacher will mark it wrong.