ABCD is a parallelogram and X is the mid-point of AB. If ar (AXCD) = 24 cm^2, then ar (ABC) = 24 cm^2.

Question

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.

Answer 1

False

Explanation:

In ΔABC, X is midpoint of AB

Considering the given question,

Hence ar(ΔAXC) = ar(ΔBXC) = ½ ar(ΔABC)

Therefore,

ar(ΔAXC) = ar(ΔBXC) = 12 cm²

Area of ||gm ABCD = 2 x ar(ΔABC)

= 2 x 24 = 48 cm²

But, according to the question,

area of ||gm ABCD = ar(AXCD) + ar(ΔBXC)

= 24 + 12 = 36 cm²

Hence, we find a contradiction here.

So, If ar (AXCD) = 24 cm², then ar (ABC) ≠ 24 cm²