#### 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

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

\[\text { We may divide the quadrilateral into two constructible triangles ABD and BCD } . \]

\[\text { Steps of Construction: } \]

\[\text { Step I: Draw BD = 6 . 6 cm }\]

\[\text { Step II: With B as the centre and radius BC = 4 cm, draw an arc }. \]

\[\text { Step III: With D as the centre and radius 6 . 4 cm, draw an arc to intersect the arc drawn in Step II at C }. \]

\[\text { Step IV: With B as the centre and radius 4 . 4 cm, draw an arc on the side BD opposite to that of C }. \]

\[\text { Step V: With D as the centre and radius 3 . 8 cm, draw an arc to intersect the arc drawn in Step IV at A }. \]

\[\text { Step VI: Join BA, DA, BC and CD }\]

\[\text { The quadrilateral ABCD so obtained is the required quadrilateral } .\]