Friday, September 5, 2008

Elearn Geometry Problem 172

Trapezoid, Midpoints, Quadrilaterals, Areas

See complete Problem 172 at:
www.gogeometry.com/problem/p172_trapezoid_quadrilaterals_area_midpoint.htm

Trapezoid, Midpoints, Quadrilaterals, Areas. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.
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4 comments:

  1. AnonymousSeptember 5, 2008 at 9:44 PM

    by Proposed Problem 170,
    [CED]=[ABCD]/2=[BAGF]

    ReplyDelete
  2. rv.littlemanAugust 28, 2020 at 12:35 AM

    - Define H and M the intersections of FG x CE and FG x DE (see problem 171)
    - From problem 170, [CED]=[ABCD]/2
    - [ABFG]=[DCFG]=[ABCD]/2
    - [ABFG]=S1+[HEM] +S2=[DCFG]=[FCH]+S+[DGM]
    - From problem 171 : [HEM] =[FCH]+[DGM]
    - Therefore S1+S2=S

    ReplyDelete
  3. MarcoFebruary 5, 2023 at 3:14 AM

    With the help of problem 170, [CED]=[ABCD]/2,
    also, it is easy to see that [ABFG]=[ABCD]/2
    So, [CED]=[ABFG], and by eliminating the blue area in between, S=S1+S2

    ReplyDelete

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