Sunday, September 7, 2008

Elearn Geometry Problem 174

Quadrilateral, Midpoint, Triangles, Area

See complete Problem 174 at:

Quadrilateral with Midpoints, Triangles, Areas. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.


  1. [BAF]+[EDC]=[BFD]+[BDE]=[BFE]+[EFD]=[EFC]+[EAF]=[EAFC]
    then S=S_1+S_2 is obvious

  2. Let AD=2a, and the distances from B, E and C to AD be b, e and c respectively.
    Well known, e=(b+c)/2 ( 1 ) (trapezoid midline property). Multiply each side of (1) by a, to get ae=(ab+ac)/2, i.e. [AED]=[AFB]+[FCD], where from the required equality is obvious.

    Best regards