In a ‖ gm ABCD, if Point P and Q are midpoints of AB and CD respectively and ar( ‖ gm ABCD) = 16cm 2 , then ar( ‖ gmAPQD) = ?

Question

Philoid · Accepted Answer

Given:

P and Q are midpoints of AB and CD respectively

ar(‖gm ABCD) = 16cm²

Now, consider the (‖gm ABCD)

Here,

Q is the midpoint of DC and P is the midpoint of AB.

∴ By joining P and Q (‖gm ABCD) is divided into two equal parallelograms.

That is, ar(‖gm ABCD) = ar(‖gmAPQD) + ar(‖gmPQCB)

ar(‖gm ABCD) = 2×ar(‖gmAPQD) (∵ar(‖gmAPQD) = ar(‖gmPQCB) )

2×ar(‖gmAPQD) = 16cm² (∵ar(‖gm ABCD) = 16cm²)

ar(‖gmAPQD) = 16/2 = 8cm²

∴ ar(‖gmAPQD) = 8cm²