geometry

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ABCD IS A PARALLELOGRAM.P IS A POINT ON SIDE CD.AREA OF TRIANGLE ADP=48 SQUARE CENTIMETRE AND AREA OF TRIANGLE BCP=30 SQUARE CENTIMETRE FIND AREA OF PARALLELOGRAM ABCD

  • geometry -

    Drop an altitude PQ to AB. So, the height of ABCD is PQ.

    The area of ABCD is AB*PQ
    The area of triangle APB is AB*PQ/2
    So, 48+30 = 78 is the rest of the area of ABCD. It is also half that area.

    Area ABCD = 156

  • geometry -

    by basic geometry:
    CP:PD = 30:48 = 5:8

    let CP=5x, and PD = 8x

    let the height between AB and CD = h
    so area of BCP + area of ADP = 5xh +8xh = 13xh = 78

    area of ABC = 13xh = 78

    area of whole thing = 78+30+48 = 156

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