See complete Problem 167 at:
www.gogeometry.com/problem/p167_parallelogram_triangle_area.htm
Parallelogram, Diagonal, Triangles, Areas. Level: High School, SAT Prep, College geometry
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Saturday, August 30, 2008
Elearn Geometry Problem 167
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Draw a line through E perpendicular to AB & CD intersecting AB in J and DC in K. Let JK = h. Now Tr ABE + Tr EDC = AB*JE/2 + CD*EK/2 =AB*h/2 since AB=CD and JK=h. But AB*h/2 = Tr ABD = Tr BDC. So Tr ABE + Tr EDC = Tr BDC = S + Tr BGF + Tr DHC. Or S = (Tr ABE-Tr BGF)+(Tr. EDC-Tr.DHC)
ReplyDelete= (S1+S2)+(S3 = S1+S2+S3
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