Question

In the given figure, PQRS is a parallelogram If SM = MR and area \(\Delta\) SPM = 25 \(cm^2\), then

(i) What is the area of \(\Delta RQM\)?

(ii) what is the area parallelogram PQRS?

R P 

Answer 1

(i) PQRS is a parallelogram and SM = MR (given)

area $\Delta PSM$ = area $\Delta QRM$

($\Delta$'s having equal bases and between the same $\parallel$'s)

area $\Delta RQM=25c{m}^2$

(ii) Draw MN $\parallel$ PS $\parallel$ RQ

If a triangle and a parallelogram are on the same base and between the same parallel, then the area of the parallelogram would be twice the area of the triangle.

Area parallelogram PNMS = 2 $\times$ area $\left(\Delta PMS\right)$

$=2\times 25$

$=50{\text{cm}}^2...\left(1\right)$

area parallelogram MNQR = 2 $\times$ area $\Delta QRM$

$=2\times 25$

$=50{\text{cm}}^2...\left(2\right)$

From (1) and (2)

area parallelogram PQRS = 50 + 50

$=100{\text{cm}}^2$