Question

In the given figure, if AB ∥ DC ∥ FG and AE is a straight line. Also, AD ∥ FC. Prove that: area of ∥ gm ABCD = area of ∥ gm BFGE.

Answer 1

Joining AC and FE, we get

ΔAFC and ΔAFE are on the same base AF and between the same parallels AF and CE.
⇒ A(ΔAFC) = A(ΔAFE)
⇒ A(ΔABF) + A(ΔABC) = A(ΔABF) + A(ΔBFE)
⇒ A(ΔABC) = A(ΔBFE)

⇒ `(1)/(2)` A(parallelogram ABCD)

= `(1)/(2)`A(parallelogram BFGE)

⇒ A(parallelogram ABCD)
= A(parallelogram BFGE).