Question

Construct a rectangle having adjacent sides of $6cm$ and $4cm$ and find its area

Answer 1

Given: Adjacent sides are $6cm$ and $4cm$.
Steps for construction
Step $1$ : Draw a rough diagram and mark the given measurements.
Step $2$ : Draw a line segment $AB=6cm$.
Step $3$ : At $A$, using a compass construct $\overrightarrow{AX}\perp \overrightarrow{AB}$.
Step $4$ : With $A$ as centre, draw an arc of radius $4cm$ and let it cut $\overrightarrow{AX}$ at $D$.
Step $5$ : With $D$ as centre, draw an arc of radius $6cm$ above the line segment $\overline{AB}$.
Step $6$ : With $B$ as centre, draw an arc of radius $4cm$ cutting the previous arc at $C$. Join $\overline{BC}$ and $\overline{CD}.ABCD$ is the required rectangle.
Step $7$ : $AB=l=6cm$ and $BC=b=4cm$.

Area of rectangle$=l\times b=6\times 4=24cmsq.$