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

AB = 8 cm, BC = 6.8 cm, CD = 6 cm, AD = 6.4 cm and ∠B = 50°.

Given. ABCD is a quadrilateral.

AB = 8 cm, BC = 6.8 cm,CD = 6 cm, AD = 6.4 cm , ∠B = 50°.

Formula used. Area of triangle = × Base × Height

Steps for construction.

Step 1 : Draw a line AB of 8cm

Step 2 : Draw an angle of 50° on point B and extend the line 6.8cm

And make the end point as C

Step 3 : Draw an arc of 6cm from point C and 6.4cm from point A

Step 4 : Mark the intersection point D and join AD and DC

Step 5 : Join A and C to divide quadrilateral in two triangles

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)

= × 6.4 × (6.6cm + 5.3cm)

= 38.08cm²

Conclusion. Hence quadrilateral ABCD is constructed and its Area is

38.08cm²