Question

(i)If the area of parallelogram PQRS is 48 cm\(^2\) and line XY || AS, then what is the area of triangle ACS?

(ii)In figure, ABCD, DCFE and ABFE are parallelograms. Show that ar(ADE)=ar( BCF)

Answer 1

(i)

$\Delta APS$ and parallelogram PQRS are on equal bases and have the same parallels.

So, Area ($\Delta APS)=\frac{1}{2}$ Area (PQRS) = 24 cm${}^2$

Triangle APS and triangle ACS are on equal base and same parallels AS and XY

So, Area $\left(\Delta ACS\right)=\left(\Delta APS\right)=24{\text{cm}}^2$

(ii)Since, ABCD is a parallelogram [Given]

$\therefore$ Its opposite sides are parallel and equal.

i.e., AD = BC …(1)

Now, $\Delta ADE$ and $\Delta BCF$ are on equal bases AD = BC ...[from (1)]

and between the same parallels AB and EF.

So, $ar\left(\Delta ADE\right)=ar\left(\Delta BCF\right)$.