Construct a quadrilateral ABCD, in which AB = 5.6cm BC = 4.5cm CD = 4.8cm DA = 3.9cm and AC = 6.8 cm

To construct quadrilateral ABCD with the given dimensions, follow these step-by-step instructions:

1. **Draw Line Segment AB**:  
   - Use a ruler to draw segment AB with a length of 5.6 cm.

2. **Draw Line Segment AC**:  
   - From point A, draw a circle with radius 6.8 cm (this represents AC).
   - From point B, draw another circle with radius 4.5 cm (this represents BC).
   - The point where these two circles intersect is point C.

3. **Draw Line Segment BC**:  
   - Now connect point B to point C with a line segment of length 4.5 cm.

4. **Draw Line Segment CD**:  
   - From point C, draw a circle with radius 4.8 cm (this represents CD).
   - From point A, draw another circle with radius 3.9 cm (this represents DA).
   - The point where these two circles intersect is point D.

5. **Draw Line Segment DA**:  
   - Finally, connect point D to point A to complete the quadrilateral.

Now, you have quadrilateral ABCD with the specified side lengths:  
- AB = 5.6 cm  
- BC = 4.5 cm  
- CD = 4.8 cm  
- DA = 3.9 cm  
- AC = 6.8 cm  

Would you like further details or any clarifications?

### 5 Related Questions:
1. How can you calculate the area of this quadrilateral?
2. What is the importance of diagonals in quadrilateral constructions?
3. How would the construction differ if angle measurements were provided?
4. Can this quadrilateral be inscribed in a circle? Why or why not?
5. How could you verify if this quadrilateral is a parallelogram?

### Tip:  
When constructing geometric figures, always double-check your circle intersections to ensure accuracy.

Learn step-by-step how to construct a quadrilateral ABCD with side lengths AB = 5.6 cm, BC = 4.5 cm, CD = 4.8 cm, DA = 3.9 cm, and diagonal AC = 6.8 cm. This guide covers geometric concepts like circle intersections and the properties of quadrilaterals, ideal for students in Grades 8-10.

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