Final answer:
The perimeter of the given polygon is 28 units, and the area is 45 square units. The polygon formed by the vertices S, T, U, and V is a rectangle with a length of 9 units and a width of 5 units.
Step-by-step explanation:
To find the perimeter and the area of a polygon with vertices S (3,0), T (3,9), U (8,9), V (8,0), we need to consider that this shape is a rectangle. The distances between the vertices can be calculated using the difference between their coordinates. The vertical sides (ST and UV) are 9 units long (9 - 0), and the horizontal sides (SU and TV) are 5 units long (8 - 3).
The perimeter (P) is the sum of all side lengths: P = 2*(length + width), which is P = 2*(9 + 5) = 2*14 = 28 units. The area (A) of a rectangle is the product of its length and width: A = length * width, so A = 9 * 5 = 45 square units.