Proposed Problem

See complete Problem 280 at:

gogeometry.com/problem/p280_quadrilateral_perpendicular_squares_areas.htm

Level: High School, SAT Prep, College geometry

## Friday, April 3, 2009

### Problem 280: Quadrilateral, Perpendiculars, Area of Squares

Labels:
area,
perpendicular,
quadrilateral,
square

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S1+S3+S5+S7 = AD^2+BE^2+CF^2+DG^2

ReplyDelete=(AO^2-OD^2)+(BO^2-OE^2)+(CO^2-OF^2)+(DO^2-OG^2)

=(BO^2-OD^2)+(CO^2-OE^2)+(DO^2-OF^2)+(AO^2-OG^2)

=BD^2+CE^2+DF^2+AG^2

=S2+S4+S6+S8

QED

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