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

AB = 6 cm, BC = 7 cm, AD = 6 cm, CD = 5 cm, and ∠BAC = 45°.

Given. ABCD is a quadrilateral.

AB = 6 cm, BC = 7 cm,AD = 6 cm, CD = 5 cm , ∠BAC = 45°

Formula used. Area of triangle = × Base × Height

Steps for construction.

Step 1 : Draw a line AB of 6cm

Step 2 : Draw an angle on point A of 45° and extend the ray to AC’

Step 3 : Make an arc of 7cm from point B and mark the point of

intersection of arc and ray AC’ as point C.

Step 4 : Draw an arc of 5cm from point C and 6cm from point A

Step 5 : Mark the intersection point D and join AD and DC

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)

= × 9.8 × (2.5cm + 4.2cm)

= 32.83cm²

Conclusion. Hence quadrilateral ABCD is constructed and its Area is

32.83cm²