Question

Construct a quadrilateral ABCD such that AB = BC = 5.5 cm, CD = 4 cm, DA = 6.3 cm and AC = 9.4 cm. Measure BD.

Answer 1

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

\[\text { Step I: Draw AB = 5 . 5 cm }\]

\[\text { Step II: With B as the centre and radius BC = 5.5 cm, draw an arc}\].

\[\text { Step III: With A as the centre and radius AC = 9.4 cm, draw an arc to intersect the arc drawn in Step II at C}\].

\[\text { Step IV: With C as the centre and radius CD = 4 cm, draw an arc}\].

\[\text { Step V: With A as the centre and radius AD = 6.3 cm, draw an arc to intersect the arc drawn in Step IV at D}\].

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

Measure of BD is 5.1 cm.

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