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

AB = 7 cm, BC = 5 cm, AC = 6 cm, CD = 4 cm, and ∠ACD = 45°.

Given. ABCD is a quadrilateral.

AB = 7 cm, BC = 5 cm, CD = 4 cm , ∠ACD = 45°, AC = 6 cm

Formula used. Area of triangle = × Base × Height

Steps for construction.

Step 1 : Draw a line AB of 7cm

Step 2 : Draw an arc of 6cm from point A and 5 cm from point B

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

Step 4 : Draw an angle of 45° on point C on AC

Step 5 : Make an arc of 4cm on ray CD’ and mark the intersection

point as D

Step 6 : Join A and D to form quadrilateral ABCD

Step 7 : 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)

= × 6cm × (4.9cm + 2.9cm)

= 23.4cm²

Conclusion. Hence quadrilateral ABCD is constructed and its Area is

23.4cm²