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Question

ABCD is a parallelogram and L is the mid point of CD. If Ar (ABCL) = 72 cm2, then find Ar (ADC).


Your Answer
A
72 cm2
Your Answer
B
144 cm2
Correct Answer
C
48 cm2
Your Answer
D
36 cm2

Solution

The correct option is C 48 cm2
Given, Ar (ABCL) = 72 cm2 and L is mid point of CD. So, CL = LD

 Ar (ABCL) = 72 cm2
Ar (ABC) + Ar (ACL) = 72 cm2
Median divides triangle into two equal halves
Ar (ACL) = Ar (ALD) = 12× Ar (ADC)
 Ar (ABC) + 12× Ar (ADC) = 72 cm2
Diagonal of a parallelogram divides it into two triangles of equal areas.
 Ar (ABC) =  Ar (ADC)
 Ar (ADC) + 12× Ar (ADC) = 72 cm2
 32× Ar (ADC) = 72 cm2
Ar (ADC) =  48 cm2

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