Construction of Quadrilateral PQRS

To construct a quadrilateral PQRS, we need to follow the given measurements and steps:

Step 1: Draw a line segment PQ of length 4 cm:
- Take a ruler and draw a line segment PQ of length 4 cm.
- Label the endpoints as P and Q.

Step 2: Construct a circle with center P and radius 6 cm:
- Place the compass point on P and open it to a radius of 6 cm.
- Draw an arc to intersect the line segment PQ at two points.
- Label one of the intersection points as R.

Step 3: Construct a circle with center Q and radius 6 cm:
- Place the compass point on Q and open it to a radius of 6 cm.
- Draw an arc to intersect the line segment PQ at two points.
- Label the other intersection point as S.

Step 4: Connect the points R and S:
- Use a ruler to draw a line segment RS, connecting the points R and S.

Step 5: Measure and verify:
- Measure the lengths of QR, PR, PS, and QS using a ruler.
- QR, PR, PS should all measure 6 cm, and QS should measure 6.5 cm.

Construction completed.

Summary:
- To construct quadrilateral PQRS, we followed the given measurements and steps.
- We drew a line segment PQ of length 4 cm and constructed circles with centers P and Q and radii 6 cm.
- The intersections of the circles with the line segment PQ gave us the points R and S.
- We connected points R and S to form the quadrilateral PQRS.
- Finally, we measured the sides QR, PR, PS, and QS to verify that they matched the given lengths.

Hard