Answer :

Given. ABCD is a quadrilateral.

ABC = 100°, ABD = 50° and CAD = 40°, AB = 4 cm, AC = 8 cm


Formula used. Area of triangle = × Base × Height


Steps for construction.


Step 1 : Draw a line AB of 4cm


Step 2 : Draw an angle of 100° on point B and extend ray BC’



Step 3 : Make an arc of 8cm from point A and intersect it on BC’


Mark intersection point of arc and ray BC’ as point C



Step 4 : Draw an another angle of 50° on point B on AB and extend


ray to BD’



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


intersect ray BD’ mark the intersection point as D



Step 6 : Join D and C 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)


= × 8cm × (3.1cm + 3.1cm)


= 24.8cm2


Conclusion. Hence quadrilateral ABCD is constructed and its Area is


24.8cm2


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