1. **Problem Statement:** Construct quadrilateral ABCD with given sides and diagonals: AB = 6.8 cm, AD = 5.8 cm, AC = 8.9 cm, BD = 7.3 cm, BC = 4.1 cm. 2. **Step 1: Draw diagonal AC.** Draw a line segment AC of length 8.9 cm. 3. **Step 2: Locate point B.** Since AB = 6.8 cm and BC = 4.1 cm, point B lies such that AB = 6.8 cm and BC = 4.1 cm. Draw arcs: - With center A and radius 6.8 cm. - With center C and radius 4.1 cm. The intersection of these arcs is point B. 4. **Step 3: Locate point D.** Since AD = 5.8 cm and BD = 7.3 cm, point D lies such that AD = 5.8 cm and BD = 7.3 cm. Draw arcs: - With center A and radius 5.8 cm. - With center B and radius 7.3 cm. The intersection of these arcs is point D. 5. **Step 4: Connect points.** Join points A to B, B to C, C to D, and D to A to complete quadrilateral ABCD. 6. **Verification:** Check all sides and diagonals with a ruler to confirm lengths: AB = 6.8 cm, BC = 4.1 cm, CD (should be consistent), DA = 5.8 cm, AC = 8.9 cm, BD = 7.3 cm. This completes the construction of quadrilateral ABCD with the given measurements.