Question

Diagonals of rhombus ABCD intersect each other at O and Eis mid-point of AB. If ar(ABCD) = 100 cm2, then ar(AOCE) equals to?

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Answer 1

Given : Diagonals of rhombus ABCD intersect each other at O and

E is mid-point of AB.

ar(ABCD) = 100 cm²

To Find : ar(AOCE)

Solution:

ABCD is a rhombus

=> ABC and ADC are congruent triangles as AC is common side and rest side are equal

so area of ΔABC  = (1/2)  area of Rhombus ABCD

=> area of ΔABC  = (1/2) * 100

=> area of ΔABC  = 50 cm²

E is the mid point of AB

=> area of   ΔACE  , and  area of   ΔBCE  = (1/2)  area of ΔABC

=>  area of   ΔACE = (1/2) * 50 = 25 cm²

as AOC is in a straight line

Hence area AOCE  =  area of   ΔACE =  25 cm²

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Answer 2

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