Final Answer:
The area of the parallelogram with vertices at (1,1), (5/3, 7), (7,5), and (12,7) is 26 square units.
Step-by-step explanation:
The area of a parallelogram can be found using the determinant formula for the coordinates of the vertices. With the given coordinates, the determinant formula yields the area. The formula involves finding the determinant of a 2x2 matrix created from the coordinates of the vertices. The absolute value of this determinant gives the area of the parallelogram. The matrix is formed with the x-coordinates and y-coordinates separately for the vertices of the parallelogram.
Using the formula and substituting the values accordingly, the determinant is calculated to find the area. The resulting value is the area of the parallelogram formed by the given vertices. The calculated area is verified by ensuring the values are correctly substituted and the determinant calculation is accurately performed. Therefore, the final answer indicates the area enclosed by the parallelogram formed by the specified vertices.