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Math Help - Parrallelogram pandemonium

  1. #1
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    Parrallelogram pandemonium

    ABCD is a parallelogram. G is the midpoint of AD and F is the midpoint of AG. The area of the parallellogram ABCD is 200cmsquared. Find the area of the quadrilateral BCGF

    please help ugently

    thankyou
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  2. #2
    MHF Contributor
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    Quote Originally Posted by googa View Post
    ABCD is a parallelogram. G is the midpoint of AD and F is the midpoint of AG. The area of the parallellogram ABCD is 200cmsquared. Find the area of the quadrilateral BCGF

    please help ugently

    thankyou
    Let x = AD
    So, AF = x/4
    And, DG = x/2

    Let h = altitude of the parallelogram where BC and AD are the bases.
    So, x*h = 200 sq.cm

    Area of any triangle = (1/2)(base)(altitude)

    The triangle ABF:
    base = AF = x/4
    altitude = h also
    So, area = (1/2)(x/4)(h) = (1/8)(hx) = (1/8)(200) = 25 sq.cm

    The triangle CDG:
    base = DG = x/2
    altitude = h also
    So, area = (1/2)(x/2)(h) = (1/4)(hx) = (1/4)(200) = 50 sq.cm

    Therefore,
    area of BCGF = 200 -50 -25 = 125 sq.cm -------answer.
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