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The area of the parallelogram with vertices \((1,2)\), \((6,3)\), \((7,8)\), and \((12,9)\) is \(24\) square units.

Would you like details on the solution or have any questions? Here are five related questions to expand your understanding:

1. How do you find the area of a parallelogram using the coordinates of its vertices?
2. What is the significance of the cross product in calculating the area of a parallelogram?
3. How can you verify that the given points form a parallelogram?
4. How does the formula for the area of a parallelogram differ from that of a triangle?
5. What are other methods to calculate the area of a parallelogram?

**Tip:** For any set of points, plotting them on a graph can help visualize the problem and understand the geometric relationships between the points.

Find the area of the parallelogram with vertices (1,2), (6,3), (7,8), and (12,9).

Learn how to find the area of a parallelogram using the coordinates of its vertices (1,2), (6,3), (7,8), and (12,9). This solution covers key geometric concepts and vector cross-product application for students in Grades 10-12.

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