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Triangles on the Same Base (Or Equal Bases) and Equal Areas Will Lie between the Same Parallels

Diagonals AC ...

Question

Diagonals AC and BD of trapezium ABCD in which AB || DC, intersect each other at O. The triangle which is equal in area to triangle BOC is

ΔADC

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ΔAOB

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ΔDOC

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ΔAOD

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Solution

The correct option is D ΔAOD

It can be observed that ΔDAC and ΔDBC lie on the same base DC and between the same parallels AB and CD.

∴ Area (ΔDAC) = Area (ΔDBC)

Subtracting the area of ΔDOC from both we get,

Area (ΔDAC) − Area (ΔDOC) = Area (ΔDBC) − Area (ΔDOC)

⇒ Area (ΔAOD) = Area (ΔBOC) (From the figure)

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