Question

Construct a quadrilateral ABCD, when AB = 4 cm, BC = 5 cm, CD = 4.5 cm, AD = 4 cm, AC = 6 cm

Answer 1

Given: Quadrilateral ABCD with sides AB = 4 cm, BC = 5 cm, CD = 4.5 cm, AD = 4 cm and diagonal AC = 6 cm.

Steps of construction:

1. Construct triangle ABC using the given sides AB = 4 cm, BC = 5 cm and diagonal AC = 6 cm.

2. Draw segment AC = 6 cm.

3. With A as center and radius AD = 4 cm, draw an arc.

4. With C as center and radius CD = 4.5 cm, draw another arc intersecting the first arc. The intersection is point D.

5. Join points D to A and D to C to complete the quadrilateral ABCD.

ABCD is constructed with the given sides and diagonal as per the steps above. This method uses the fact that the diagonal AC divides the quadrilateral into two triangles ABC and ADC, which are constructed first, then combined by locating D using arcs from A and C with the given side lengths AD and CD.