Question

If E, F G and H are respectively the midpoints of the sides AB, BC, CD and AD of a parallelogram ABCD, show that ar(EFGH) =1/2 ar(ABCD)

Answer 1

hlo

hope the attachment will help u.

Answer 2

Hello Mate!

Given : E, F G and H are respectively the midpoints of the sides AB, BC, CD and AD of a ||gm ABCD.

To prove : ar(EFGH) =½ ar(ABCD)

To construct : Join EG.

Proof : Since AD || EG and AE || GD, so AEGD is ||gm.

Hence ar(∆EHG) = ½ ar(||gm AEGD)_(i)

Similarly, BE || GC and EG || BC, so BEGC is ||gm.

Hence ar(∆EFG) = ½ ar(||gm BEGC) _(ii)

Adding equation (i) and (ii) we get,

ar(∆EHG) + ar(∆EFG) = ½ ar(||gm AEGD) + ½ ar(||gm BEGC)

ar(EFGH) = ½ ar(ABCD)

Hence proved

Have great future ahead!