Draw quadrilateral ABCD with the following measurements. Find also its area.

AB = 5.5 cm, BC = 4.5cm, AC = 6.5 cm, ∠CAD = 80°,∠ACD = 40°

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