Constuction a quarilateral \( A B C D \) in which \( 5.1 \mathrm{~cm}, B C=4.6 \mathrm{~cm}, C D=39 \mathrm{~cm}, A D=4.5 \mathrm{~cm} \) Ac-s and diagnal \( A C=6.3 \)

To construct the quadrilateral \( ABCD \) with the given side lengths and diagonal, follow these steps: 1. **Draw the Base**: Start by drawing line segment \( BC \) which is \( 4.6 \, \text{cm} \) long. 2. **Construct Point A**: - From point \( B \), use a compass to draw an arc with a radius of \( 5.1 \, \text{cm} \) (the length of side \( AB \)). - From point \( C \), draw another arc with a radius of \( 6.3 \, \text{cm} \) (the length of diagonal \( AC \)). - The intersection of these two arcs will give you point \( A \). 3. **Construct Point D**: - From point \( A \), draw an arc with a radius of \( 4.5 \, \text{cm} \) (the length of side \( AD \)). - From point \( C \), draw another arc with a radius of \( 3.9 \, \text{cm} \) (the length of side \( CD \)). - The intersection of these two arcs will give you point \( D \). 4. **Connect the Points**: Finally, connect points \( A \) to \( B \), \( B \) to \( C \), \( C \) to \( D \), and \( D \) to \( A \) to complete the quadrilateral \( ABCD \). Make sure to check the lengths of all sides and the diagonal to ensure they match the given measurements.