Friday, September 18, 2009

Problem 357. Square, Exterior point, Triangles, Area

Proposed Problem
Click the figure below to see the complete problem 357 about Square, Exterior point, Triangles, Area.

 Problem 357. Square, Exterior point, Triangles, Area.
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Complete Problem 357
Level: High School, SAT Prep, College geometry

2 comments:

  1. 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:
    S↓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.

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  2. Draw EPF//BC, E on AB extended and F on DC extended

    Let EP = x and EB = y

    So S1 = xa/2, S3 = (a-x)a/2,
    S2 = ya/2 and S4 = (a+y)a/2

    So S1+S3 = S4-S2= a^2/2 = S/2

    Sumith Peiris
    Moratuwa
    Sri Lanka

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