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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Draw EF.

ReplyDeleteEF=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

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

ReplyDeletePer 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