Proposed Problem
Click the figure below to see the complete problem 357 about Square, Exterior point, Triangles, Area.
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Complete Problem 357
Level: High School, SAT Prep, College geometry
Friday, September 18, 2009
Problem 357. Square, Exterior point, Triangles, Area
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Let l be the side of the square ABCD and h1, h2, h3, h4 be respectively the heights of triangles PAB, PBC, PCD, PDA. We have:
ReplyDeleteS↓1=lh↓1/2, S↓2 = lh↓2/2, S↓3=l h↓3/2, S↓4=l h↓4/2. Therefore:
S↓1+ S↓3=l(h↓1+ h↓3)/2= l↑2./2,
S↓4- S↓2=l(h↓4- h↓2)/2= l↑2./2.
QED, Ianuarius.