Question

In the given figure, ABCD is a parallelogram. E is a point in CD. AE and BC are produced to meet at F.

If area of $\Delta ADF=45c{m}^2$, then area $\Delta ABE$ =___ $c{m}^2$.

• A. 90
• B. 75
• C. 45
• D. 22.5

Answer 1

The correct option is C 45

ABCD is a ||gm

area $\Delta ADF=\frac{1}{2}$ Area ||gm ABCD...(i)

(Since $\Delta$ ADF and ||gm ABCD lie on same base AD and between same parallels, area of $\Delta$ ADF is equal to half the area of ||gm ABCD.)

area $\Delta AEB=\frac{1}{2}$ area ||gm ABCD...(ii)

($\because \Delta$ and ||gm on the same base and between the same parallels)

From (i) and (ii)

$\therefore$ area $\Delta AEB$ = area $\Delta ADF$
= 45 cm${}^2$