maths --plse help me..

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ABCD IS A PARALLELOGRAM, G IS THE POINT ON AB SUCH THAT AG = 2GB, E IS A POINT OF CD SUCH THAT CE = 2DE AND AND F IS A POINT OF BC SUCH THAT BF = 2FC. PROVE THAT
1) ar(EGB) = 1/6 ar(ABCD)
2)ar(EFC) = 1/2 ar(EBF)
3) ar(EBG) = ar(EFC)
4) FIND WHAT PORTION OF THE ARE OF PARALLELOGRAM IS THE AREA OF EFG.

  • maths --plse help me.. -

    1)
    height h of ABCD and EGB is the same
    base of EGB = 1/3 AB
    area(ABCD) = h*AB
    area(EGB) = 1/2 h*(1/3 AB) = 1/6 h*AB

    2)
    base of EFC = 1/2 base of EBF
    so area is 1/2 as well

    3)
    if g = altitude from AD to BC
    area(EFC) = 1/2 * (2/3 g) * (1/3 BC) = 1/9 area(ABCD)
    So, I get area(EFC) = 2/3 area(EBG)
    Is there a typo here?

    4)
    area(EFG) = area(EGB)+area(EBF)+area(EFC)
    = 1/6(ABCD)+2area(EFC)+area(EFC)
    = 1/6(ABCD) + 3(1/9 ABCD)
    = 1/2(ABCD)

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