Final answer:
The perimeter of the square formed by the given vertices is 12 units while the area is 9 square units.
Step-by-step explanation:
The student is asked to find the perimeter and the area of a polygon with the given vertices: C (1,1), D (1,4), E (4,4), F (4,1). The shape described by these vertices is a rectangle, specifically a square since all sides are equal. The distance between two points that share the same x-coordinate or y-coordinate in a plane can be found by subtracting the shared coordinate from the other, this gives us the length of one side. In this case, the distance between C and D (or E and F) is 3 units and between D and E (or C and F) is also 3 units.
Using the fact that the perimeter of a square is four times the length of one side, we calculate the perimeter as 4 × 3 = 12 units. For the area of the square, we can simply multiply the length of one side by itself, yielding 3 × 3 = 9 square units as the area of the square.