Question

In the given figure, PQRS is a parallelogram If SM = MR and area $\Delta SPM=15c{m}^2$, then area parallelogram PQRS = ______ $c{m}^2$

• A. 30
• B. 45
• C. 60
• D. 90

Answer 1

The correct option is C 60

PQRS is a ||gm and SM = MR (given)

area $\Delta PSM$ = area $\Delta QRM$
$({\Delta }^{\prime }s$ having equal bases and between the same ||'s)

$\therefore$ area $\Delta QRM=15c{m}^2$

Draw MN || PS || RQ

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

area ||gm PNMS $=2\times$ area $\Delta PMS$
$=2\times 15$
$=30c{m}^2$...(1)

area || gm MNQR $=2\times$ area $\Delta QRM$
$=2\times 15$
$=30c{m}^2$...(2)

From (1) and (2)
$\therefore$ area || gm PQRS = 30 + 30
$=60c{m}^2$