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Question
ABCD is a parallelogram and X is the mid-point of AB. If ar (AXCD) = 24 cm2, then ar (ABC) = 24 cm2.
Options
True
False
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Solution
This statement is False.
Explanation:
Given in the question, ABCD is a parallelogram and X is the mid-point of AB.
So, area(ABCD) = area(AXCD) + area(ΔXBC) ...(i)
Now, diagonal AC of a parallelogram divides it into two triangles of equal area.
area(ABCD) = 2area(ΔABC) ...(ii)
Similarly, X is the mid-point of AB,
So, area(ΔCXB) = `1/2`area(ΔABC) ...(iii) [Median divides the triangle in two triangles of equal area]
2area(ΔABC) = `24 + 1/2` area(ΔABC) ...[By using equation (i), (ii) and (iii)]
Now, 2area(ΔABC) – `1/2`area(ΔABC) = 24
`3/2`area(ΔABC) = 24
Therefore, area(ΔABC) = `(2 xx 24)/3` = 16 cm2.
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