Answer :

Given. ABCD is a quadrilateral.

AB = 5.5 cm, BC = 6.5 cm , BD = 7 cm, AD = 5 cm , ∠BAC = 50°.

Formula used. Area of triangle = × Base × Height

Steps for construction.

Step 1 : Draw a line AB of 5.5cm

Step 2 : Make an angle of 50° on point A and extend the ray to AC’

Step 3 : Make an arc of 6.5cm from point B and mark the point of

intersection of arc and ray AC’ as point C.

Step 4 : Draw an arc of 7cm from point B and 5cm from point A

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

Step 6 : Join C and D to form quadrilateral ABCD

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)

= × 8.5cm × (2.8cm + 4.2cm)

= 29.75cm^{2}

Conclusion. Hence quadrilateral ABCD is constructed and its Area is

29.75cm^{2}

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