in a traphezium ABCD AB parallel to DC and AO : OC = 2:3 if the area of traingle AOB is 48cm² find the area of traingle DOC
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In ΔAOB & ΔDOC
angle 1= angle 2 (alternate angles)
angle 3=angle4 ( vertically opposite angles)
therefore,
ΔAOB ~ ΔDOC (by AA criteria)
therefore,
AO/OC = BO/OD (cpst)
since triangles are similar
therefore
area ΔAOB/areaΔDOC = AO²/OC²
48/area ΔDOC= (2/3)²
48/areaΔDOC = 4/9
area Δ DOC= 48*9/4= 12*9
area ΔDOC= 108cm²
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