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