Question

construct a quadrilateral ABCD in which AB=4.5cm,BC=4cm,CD=6.5cm,DA=3cm,DB=6.5cm

Answer 1

First we draw a rough sketch of a quadrilateral ABCD and write down its dimensions as shown. We may divide it into two conveniently constructible Δs ABC and ACD.

               

            Steps of construction:

            1.   Draw AC = 7 cm.

            2.   With A as centre and radius 4.5 cm, draw an arc (below AC).

            3.   With C as centre and radius 5.5 cm, draw another arc cutting the previous arc at B.

               

            4.   Join AB and BC

            5.   With A as centre and radius 6 cm, draw an arc (above AC).

            6.   With C as centre and radius 4 cm, draw another arc cutting the previous arc and D.

            7.   Join AD = CD.

            Then, ABCD is the required quadrilateral