#### 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.

#### Solution

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

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

\[\text { Step II: With B as the centre and radius BC = 5 . 5 cm, draw an arc }. \]

\[\text { Step III: With A as the centre and radius AC = 9 . 4 cm, draw an arc to intersect the arc drawn in Step II at C }. \]

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

\[\text { Step V: With A as the centre and radius AD = 6 . 3 cm, draw an arc to intersect the arc drawn in Step IV at D } . \]

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

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

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Solution 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. Concept: Constructing a Quadrilateral - When Two Diagonals and Three Sides Are Given.