What is the process to calculate the area of a parallelogram given its vertices at points K(123), L(136), and M(386)?

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Calculating the Area of a Parallelogram Given Its Vertices

To find the area of a parallelogram with given vertices, we can use the formula based on the coordinates of its vertices. However, in the case of your provided vertices (K(123), L(136), M(386)), we first need to establish all four vertices of the parallelogram. Assuming that your points represent three consecutive vertices, we will need to find the fourth vertex using vector addition.

Step 1: Identify the Coordinates

The points are as follows:

  • K(123)
  • L(136)
  • M(386)

Step 2: Determine the Fourth Vertex (N)

To find the fourth vertex, we can use the properties of the parallelogram where opposite sides are equal in length and direction. Let’s denote the unknown point as N. The vertex N can be found using the relationship:

N = K + (M - L)

This results from the parallelogram law which states that the diagonal divides the parallelogram into two congruent triangles.

Step 3: Calculate the Area

Once all four vertices are established, we can compute the area. The area of a parallelogram can be calculated using the formula:

Area = base × height

Alternatively, you can also use the formula derived from the determinant of a matrix formed by the coordinates:

Area = |(x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2))| / 2

For the specifics:

  1. List the coordinates of the vertices in order.
  2. Apply the area formula based on the selected coordinates.

Conclusion

Following these steps, you will accurately find the area of the parallelogram with the provided vertices. Ensure to calculate the coordinates correctly to achieve the right area.

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