Question

Construct a trapezium ABCD in which AB || DC, AB = 4.4 cm, ∠ABC = 90°, ∠DAB = 120° and the distance between parallel sides is 3.5 cm.

Answer 1

Given:

AB || DC, AB = 4.4 cm

∠ABC = 90°

∠DAB = 120°

Distance between the parallel sides (height) = 3.5 cm

Step-wise calculation and construction:

1. Place AB horizontally:

Draw AB = 4.4 cm. 

Label A (left) and B (right).

2. Draw the top parallel line through points at distance 3.5 cm from AB:

From any point on AB, construct a line parallel to AB at a perpendicular distance of 3.5 cm. Use a compass to transfer the 3.5 cm distance and draw a line parallel to AB. This is the line that will contain DC.

3. Locate C:

Through B construct BC ⊥ AB because ∠ABC = 90°.

The intersection of this perpendicular with the top parallel is C.

Hence, BC = 3.5 cm.

4. Locate D:

At A construct ∠DAB = 120° measure 120° counterclockwise from AB. Draw the ray from A at 120°.

The intersection of this ray with the top parallel is D.

5. Join AD and CD to complete trapezium ABCD.