A Parallelogram and a Triangle between the Same Parallels
ABCD is a par...
Question
ABCD is a parallelogram and L is the mid point of CD. If Ar (ABCL) = 72 cm2, then find Ar (ADC).
A
72 cm2
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B
144 cm2
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C
48 cm2
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D
36 cm2
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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