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The area of a triangle ABC is 24. D,
E, and F are the midpoints of BC, AC, and AB, respectively.
Perpendiculars from E to AB and F to AC meet at G,
perpendiculars from F to BC and D to AB meet at H,
perpendiculars from D to AC and E to BC meet at M. Find the area
of the hexagon DMEGFH.
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