See complete Problem 174 at:

www.gogeometry.com/problem/p174_quadrilateral_area_midpoint.htm

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

Post your solutions or ideas in the comments.

## Sunday, September 7, 2008

### Elearn Geometry Problem 174

Labels:
area,
midpoint,
quadrilateral,
triangle

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[BAF]+[EDC]=[BFD]+[BDE]=[BFE]+[EFD]=[EFC]+[EAF]=[EAFC]

ReplyDeletethen S=S_1+S_2 is obvious

Let AD=2a, and the distances from B, E and C to AD be b, e and c respectively.

ReplyDeleteWell 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.

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