Q. 85.0( 1 Vote )

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

AB = 5 cm, BD = 7 cm, BC = 4 cm, ∠BAD = 100° and ∠DBC = 60.

Answer :

Given. ABCD is a quadrilateral.

∠BAD = 100° and ∠DBC = 60.

AB = 5 cm, BC = 4 cm, BD = 7 cm

Formula used. Area of triangle = × Base × Height

Steps for construction.

Step 1 : Draw a line AB of 5cm

Step 2 : Make an angle of 100° on point A and extend the ray to AD’

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

intersection point as D

Step 4 : Make an angle of 60° on point B on BD and extend ray BC’

Step 5 : Mark an arc of 4cm from point B on BC’ and name the

intersection point as C.

Step 6 : Join C and D to form Quadrilateral ABCD

Step 6 : Draw perpendicular from A and C on BD and name the intersecting point as E and F respectively

Area of quadrilateral = Area of ΔABD + Area of ΔCBD

= × AE × BD + × CF × BD

= × BD × (AE + CF)

= × 7cm × (3.5cm + 2.9cm)

= 22.4cm^{2}

Conclusion. Hence quadrilateral ABCD is constructed and its Area is

22.4cm^{2}

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