# Construct a quadrilateral ABCD in which AB = 4.4 cm,

Question:

Construct a quadrilateral ABCD in which AB = 4.4 cm, BC = 4 cm, CD = 6.4 cm, DA = 3.8 cm and BD = 6.6 cm.

Solution:

First, we draw a rough sketch of the quadrilateral $\mathrm{ABCD}$ and write down its dimensions along the sides.

We may divide the quadrilateral into two constructible triangles $\mathrm{ABD}$ and $\mathrm{BCD}$.

Step I : Draw $\mathrm{BD}=6.6 \mathrm{~cm}$

Step II : With $\mathrm{B}$ as the centre and radius $\mathrm{BC}=4 \mathrm{~cm}$, draw an arc.

Step III : With $\mathrm{D}$ as the centre and radius $6.4 \mathrm{~cm}$, draw an arc to intersect the arc drawn in Step II at C.

Step IV : With B as the centre and radius $4.4 \mathrm{~cm}$, draw an arc on the side BD opposite to that of C.

Step V: With D as the centre and radius $3.8 \mathrm{~cm}$, draw an arc to intersect the arc drawn in Step IV at A.

Step VI : Join BA, DA, BC and CD

The quadrilateral ABCD so obtained is the required quadrilateral.