Geometry Problems, Online Education
Online Geometry Problem 862: Trapezoid, Parallel, Equal Areas, RMS, Root Mean Square. Level: High School, College, Mathematics Education

The figure below shows a trapezoid ABCD with EF parallel to BC = a, and AD = b. If area AEFD = area EBCF, prove that EF is the root mean square of a and b, that is, Formula to prove.

 

Problem862: Trapezoid, Parallel, Equal Areas, RMS, Root Mean Square
 


 

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." 

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