Answer :

Given. ABCD is a quadrilateral.

AB = 5 cm, BC = 6 cm, CD = 4 cm, DA = 5.5 cm, AC = 7 cm

Formula used. Area of triangle = × Base × Height

Steps for construction.

Step 1 : Draw a line AB of 5cm

Step 2 : Draw an arc of 7 cm from point A and 6 cm from point B

Step 3 : Make the intersection point C and join AC and BC

Step 4 : Draw an arc of 4cm from point C and 5.5cm from point A

Step 5 : Mark the intersection point D and join AD and DC

Step 6 : Draw perpendicular from B and D on AC and name the intersecting point as E and F respectively

Area of quadrilateral = Area of ΔACB + Area of ΔACD

= × BE × AC + × DF × AC

= × AC × (BE + DF)

= × 7cm × (4.2cm + 3.1cm)

= 25.55cm^{2}

Conclusion. Hence quadrilateral ABCD is constructed and its Area is

25.55cm^{2}

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