Question

Construct a rhombus $ABCD$ with $AB=7cm$ and $\angle A={60}^{\circ }$ and find its area

Answer 1

Given: $AB=7cm$ and $\angle A={60}^{\circ }$.
Steps for construction
Step $1$ : Draw a rough diagram and mark the given measurements.
Step $2$ : Draw a line segment $AB=7cm$.
Step $3$ : At $A$ on $\overline{AB}$ make $\angle BAX$ whose measure is ${60}^{\circ }$.
Step $4$ : With $A$ as centre draw an arc of radius $7cm$. This cuts \vec {AX} at $D$.
Step $5$ : With $B$ and $D$ as centres draw arcs of radius $7cm$ and let them cut each other at $C$.
Step $6$ : Join $\overline{BC}$ and $\overline{DC}$.
$ABCD$ is the required rhombus.
Step $7$ : Measure the lengths $AC$ and $BD$.
$AC=d_1=12.2cm$ and $BD=d_2=7cm$.