Final answer:
The area of circle c, which passes through points w and z, can be found using the area formula for a circle once the radius is known. Since the question lacks specific measurement details, an exact answer can't be given without additional information.
The correct option is not given.
Step-by-step explanation:
The question involves finding the area of a circle that passes through points w and z, given that points w, x, c, y, and z all lie on the same line segment wz. To solve this, we need to understand that the distance between points w and z represents the diameter of circle c since it passes through both points, and point c is the center of the circle.
The area of a circle is calculated using the formula Area = πr^2, where r is the radius of the circle. Since the distance wz is the diameter, the radius would be half of this distance. Assuming the value of wz is given, or can be deduced from additional information (which seems to be missing in the provided question), we can calculate the radius r and then the area.
However, given the options presented (81m units, 164m units, 324m units, 1296m units), it seems that the radius or the diameter has already been calculated and we just need to apply the area formula correctly.
The correct option is not given.