Question

Construct a parallelogram ABCD, when AB = 4.5 cm, BC = 5.5 cm and altitude on BC = 3.5 cm.

Answer 1

Given:

• AB = 4.5 cm
• BC = 5.5 cm
• Altitude on BC = 3.5 cm

Steps of construction:

1. Draw the base BC = 5.5 cm.
2. At points B and C, draw perpendicular lines to BC (these represent altitudes).
3. From B and C, measure 3.5 cm along the perpendiculars and mark points P and Q respectively.
4. Join points P and Q to form a line parallel to BC at the given altitude.
5. On line PQ, from point B, mark point A such that AB = 4.5 cm.
6. Similarly, from point C on line PQ, mark point D such that CD = 4.5 cm (since opposite sides of a parallelogram are equal).
7. Join points A to B, B to C, C to D and D to A.

The quadrilateral ABCD constructed in this manner is a parallelogram with sides AB = 4.5 cm, BC = 5.5 cm and the altitude on BC equal to 3.5 cm.