# Math Help - Trapezoid problem I know the answer to

1. ## Trapezoid problem I know the answer to

In trapezoid ABCD, AB = 2, BC = 6, CD = 10, and DA = 6. Points F and G are the midpoints of line AD and line BC, respectively. Line FG intersects line BD and line AC, respectively, at H and J, and line AC intersects line BD at point E. Compute the area of triangle EHJ. I know the answer is 4radical5/3, but desperately need someone to explain how this answer is reached.

2. Here is one way.

(1) Note that the trapezoid is isosceles.

(2) Find FG.

(3) Find FH and JG; thus, find HJ.

(4) Let A' and B' be projections of A and B, respectively, on DC. Since AD = BC, we have A'D = B'C. Find A'D and B'C.

(5) Find the height of the trapezoid AA' (and BB').

(6) Let E' be the projection of E to DC; then DE' = E'C = 5. The triangles DEE' and DBB' are similar. Find EE'.

(7) The area of EHJ is 1/2 (EE' - 1/2 AA') * HJ.