Question

Construct a quadrilateral ABCD, when AB = 3.5 cm, BC = 4 cm, CD = 4.5 cm, AC = BD = 6 cm

Answer 1

Given:

• AB = 3.5 cm
• BC = 4 cm
• CD = 4.5 cm
• AC = BD = 6 cm (both diagonals are equal)

Steps of construction:

1. Draw the diagonal AC = 6 cm.

2. With A as center and radius 3.5 cm, draw an arc.

3. With C as center and radius 4.5 cm, draw another arc intersecting the previous arc at point D.

4. Join CD.

5. With C as center and radius 4 cm, draw an arc.

6. With A as center and radius 3.5 cm, draw another arc intersecting the previous arc at point B.

7. Join AB and BC.

8. Finally, join BD.

Since both diagonals AC and BD are equal (6 cm), and the sides are as given, the intersection of the arcs locates points B and D correctly.

The quadrilateral ABCD constructed with AB = 3.5 cm, BC = 4 cm, CD = 4.5 cm, and diagonals AC = BD = 6 cm is thus obtained by first drawing diagonal AC then locating points B and D by intersecting arcs as per the given side lengths and joining the points accordingly.