Answer :

Given. ABCD is a quadrilateral.

AB = 5.5 cm, BC = 4.5cm, AC = 6.5 cm


CAD = 80° and ACD = 40°


Formula used. Area of triangle = × Base × Height


Steps for construction.


Step 1 : Draw a line AB of 5.5cm


Step 2 : Draw an arc of 6.5 cm from point A and 4.5cm from point B



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



Step 4 : Make an angle of 80° on point A on AC and extend ray AD’



Step 5 : Make an angle of 40° on point C on AC and extend to


intersect at ray AD’ and mark the intersection point as D



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)


= × 6.5cm × (4.7cm + 3.8cm)


= 27.625cm2


Conclusion. Hence quadrilateral ABCD is constructed and its Area is


27.625cm2


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