# Online Geometry Problem 880: Triangle, Midpoints, Sides, Perpendiculars, Hexagon, Area. Level: High School, Honors Geometry, College, Mathematics Education

 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.     Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."
 Home | Search | Geometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | Problems Art Gallery |  Art | 871-880 | Triangle | Hexagon | Midpoint | Perpendicular | Parallelogram | Area | Triangle area | Solution / comment | By Antonio Gutierrez