Question

Construct a rhombus $PQRS$ with $PR=8cm$ and $QS=6cm$ and find its area.

Answer 1

Given: $PR=8cm$ and $QS=6cm$.
Steps for construction
Step $1$: Draw a rough diagram and mark the given measurements.
Step $2$ : Draw a line segment $PR=8cm$.
Step $3$ : Draw the perpendicular bisector $\overrightarrow{XY}$ to $\overline{PR}$. Let it cut $\overline{PR}$ at $"O"$.
Step $4$ : With $O$ as centre and $3cm$ (half of $QS$) as radius draw arcs on either side of ${}^{\prime }{O}^{\prime }$ which cuts $\overrightarrow{XY}$ at $Q$ and $S$ as shown in fig.
Step $5$ : Join $\overline{PQ},\overline{QR},\overline{RS}$ and $\overline{SP}$.
$PQRS$ is the required rhombus.
Step $6$ : We know, $PR=d_1=8cm$ and $QS=d_2=6cm$.
Calculation of area:
In the Rhombus $PQRS$,
$d_1=8cm$ and $d_2=6cm$.
Area of the rhombus $PQRS$
$=\frac{1}{2}\times d_1\times d_2$
$=\frac{1}{2}\times 8\times 6$
$=24c{m}^2$.