Question

In parallelogram ABCD, rhombus PQRS is constructed by joining midpoints of the sides. Find area of the rhombus if AB and BC are 8 cm and 6 cm respectively.

• A. 12 $c{m}^2$
• B. 24 $c{m}^2$
• C. 36 $c{m}^2$
• D. 48 $c{m}^2$

Answer 1

The correct option is B 24 $c{m}^2$

Given : ABCD is a parallelogram,
AB= 8 cm, BC= 6 cm.
PQRS is a rhombus.

As the rhombus is made from joining the midpoints AD=PR=BC and also they are parallel to each other, similarly AB=SQ=DC and they are also parallel to each other.

we know area of rhombus
= $\frac{1}{2}$$\times$(product of diagonals)
= $\frac{1}{2}$$\times$(PR$\times$SQ)
= $\frac{1}{2}$$\times$(6$\times$8) .....(PR=BC, AB=SQ)
= $\frac{48}{2}$ = 24 $c{m}^2$