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Question

Question 1
Write True or False and justify your answer :
ABCD is a parallelogram and X is the mid - point of AB. If ar (AXCD) = 24 cm2, then ar (ABC) = 24 cm2

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Solution

False.
Given, ABCD is a parallelogram and ar (AXCD) = 24 cm2

Let area of the parallelogram ABCD is 2y cm2.
Join AC.


We know that, diagonal divides the area of parallelogram in two equal areas.
ar (ABC) = ar (ACD) = y
So, ar (ACX) = ar (BCX) [since, x is median in ABC]
=12ar(ABC)=12y
Now, ar (AXCD) = ar (ADC) + ar (ACX)
24=y+y2
24=3y2
ar(ΔABC)=16 cm2

Therefore, given statement is false.

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