Question

Construct a rhombus $ABCD$ with $AC=7.5cm$ and $\angle A={100}^{\circ }$. Find its area

Answer 1

Given: $AC=7.5cm$ and $\angle A={100}^{\circ }$.
Steps for construction
Step $1$ : Draw a rough figure and mark the given measurements.
Step $2$ : Draw a line segment $AC=7.5cm$.
Step $3$ : At A draw $\overrightarrow{AX}$ and $\overrightarrow{AY}$ on either side of $\overline{AC}$ making an angle ${50}^{\circ }$ with $\overline{AC}$.
Step $4$ : At $C$ draw $\overrightarrow{CM}$ and $\overrightarrow{CN}$ on either side of $\overline{CA}$ making an angle ${50}^{\circ }$ with $\overline{CA}$.
Step $5$ : Let $\overrightarrow{AX}$ and $\overrightarrow{CM}$ cut at $D$ and $\overrightarrow{AY}$ and $\overrightarrow{CN}$ cut at $B$.
$ABCD$ is the required rhombus.
Step $6$ : Measure the length $BD.BD=d_2=9cm.AC=d_1=7.5cm$.