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Math Help - Trapezoid problem I know the answer to

  1. #1
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    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.
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  2. #2
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    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.
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