Question
Construct, if possible, a quadrilateral $ABCD$ given $AB = 6\ cm, BC = 3.7\ cm, CD = 5.7\ cm, AD = 5.5\ cm$ and $BD = 6.1\ cm$. Give reasons for not being able to construct it, if you cannot.
✓
Answer
Steps of construction:
Step $I$: Draw $AB = 6\ cm$.
Step $II$: With $A$ as the centre and radius $5.5\ cm$, draw an arc.
Step $III$: With $B$ as the centre and radius $6.1\ cm$, draw an arc to intersect th arc drawn in Step $II$ at $D$.
Step $IV$: With $B$ as the centre and radius $3.7\ cm$, draw an arc on the side.
Step $V$: With $D$ as the centre and radius $5.7\ cm$, draw an arc to intersect the arc drawn in Step $IV$ at $C$.
Step $VI$: Join $BD, DA, BC$ and $CD$. The quadrilateral $ABCD$ so obtained is the required quadrilateral.
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