Question

ABCD is a parallelogram, E and F are the mid-points of BC and CD respectively. Prove that: ar (∆AEF) = 3/8 ar (||gm ABCD)

Answer 1

Given: ABCD is a parallelogram in which E and F are the mid-points of sides BC and CD respectively.

To prove: ar (∆AEF) = \(\frac { 3 }{ 8 }\) ar (||gm ABCD)

Construction: Join BD and EF.

Proof: In ∆BCD, E is the mid-point of BC and F is the mid-point of CD

Since, parallelogram ABCD and ∆ABE are in between the same parallel lines AD and BC and BE = 1/2BC