Draw a parallelogram ABCD, with AB = 7 cm, AD = 6 cm and ∠DAB = 45°.

Draw the perpendicular bisector of side AD and let it meet AD at point P. Also, draw the diagonals AC and BD, and let them intersect at point O. Join O and P. Measure OP.

Steps:

1. Draw AB = 7 cm.

2. At A, construct angle GAB = 45° and from GA cut DA = 6 cm.

3. Taking B as center, draw an arc of radius 6 cm (= AD) and taking D as center draw one more arc of radius 7 cm (= AB). Let the two arcs intersect at point C.

4. Join DC and BC.
   ABCD is the required parallelogram.

5. With A as center, and radius equal to more than half of AD, draw arcs on both sides of AD.

6. With D as center and with the same radius as taken in step 5, draw arcs on both the sides of AD.

7. Let the arcs intersect each other at X and Y.

8. Join X and Y.

9. The line XY intersects the line AD at P.

10. Join BD and AC and they intersect each other at O.

Hence, the length of OP = 3.5 cm.