# Abcd is a trepizeum with ab parallel dc x and y are the mid points ad and bc respectively if cd is equal to 30cm and ab is equal to 50cm show that area of (dcyx) is equal to 7/9 of area of (xyba)

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by razaarshad78

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by razaarshad78

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let it intersect xy in e

by M.P.T,xe=1/2*50=25 and ey=15

hence,xy=25+15=40

draw a perpendicular from the top vertex

height of abxy=that of dcxy

now,

ar.of a trapezium=1/2*h*(a+b)

thus,

ar.abyx=1/2*h*(50+40)

ar.dcxy=1/2*h*(30+40)

area of dcyx/ar.abyx= [1/2*h*70]/[1/2*h*90]=70/90=7/9