Z8–I–5 MO 2019

For eight different points as shown in the figure: points C, D, and E lie on a line parallel to line AB; F is the midpoint of segment AD; G is the midpoint of segment AC; and H is the intersection of lines AC and BE. The area of triangle BCG is 12 cm² and the area of quadrilateral DFHG is 8 cm².

Determine the areas of triangles AFE, AHF, ABG, and BGH.

Final Answer:

S1 =  12 cm2
S2 =  12 cm2
S3 =  4 cm2
S4 =  4 cm2

Step-by-step explanation:

S(BCG) = 12  cm2 S(DFHG)= 8  cm2  S =  2av   S1 = S(AFE) = S(BCG) S1=12=12 cm2
S2 = S(ABG) =S(BCG)=  S1 S2=S1=12=12 cm2
S(ABD) = 2 S(BCG) = 2 12 = 24  S3 = S(AHF) = S(ABD)  S(DFHG)  S(ABG)  S3=24812=4 cm2
S4 = S(BGH) = S(AHF) S4=S3=4=4 cm2



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