Wednesday, July 17, 2024

Find the Area of Quadrilateral BGDJ in a Right Triangle

Challenging Geometry Puzzle: Problem 1564. Share your solution by posting it in the comment box provided.
Audience: Mathematics Education - K-12 Schools, Honors Geometry, and College Level.

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Illustration of Geometry Problem 1564

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Posted by Antonio Gutierrez at 2:05 PM
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2 comments:

  1. Georgios Kousinioris, Gastouni GreeceJuly 20, 2024 at 12:29 AM

    Draw EF.
    EF=BD=8 (see pr.1562) and GJ=EF/2=4
    GJ┴BD (see pr. 1563)
    Quadrilateral BGDJ has perpendicular diagonals so
    AreaBGDJ=(BDxGJ)/2=4x8/2=16

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  2. Peter TranJuly 23, 2024 at 11:12 AM

    https://photos.app.goo.gl/zRqFoqBZgQQpMNLN7


    Per the result of problem 1562
    We have EBFD is a square and EF=BD & EF ⊥ BD
    G and J are midpoints of EH & HF
    So GJ=½. EF and EF⊥BD
    Area of BGDJ= ½. BD.JG= ½. 8.4= 16

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