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)

= 24.8cm^{2}

Conclusion. Hence quadrilateral ABCD is constructed and its Area is

24.8cm^{2}

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