Question

In the given figure AF = BF and DCBF is a parallelogram. If the area of ΔABC is 30 square units, find the area of the parallelogram DCBF.

Answer 1

In ΔABC,
AF = FB and EF || BC  ...(given)
∴ AE = EC                ...(Converse of Midpoint theorem) ...(i)
In ΔAEF and ΔCED,
∠FEA = ∠DEC     ...(Vertically opposite angles)
CE = AE               ...[From (i)]
∠FAE = ∠DCE    ...(Alternate angles)
∴ ΔFAE ≅ ΔCED  ...( ASA test of congruency)
⇒ A(ΔAEF) = A(ΔCED)  ....(ii)
A(ΔABC)
= A(ΔAEF) + A(EFBC)
= A(ΔCED) + A(EFBC)  ....[From (ii)]
∴ A(ΔABC) = A(||^gm DCBF)
⇒ A(||^gm DCBF) = 30 sq. units.