Final answer:
The area and perimeter of the rectangle are 56 square units and 30 units respectively. They were calculated using the given vertices of the rectangle and the formulas for the area and perimeter of a rectangle, respectively.
Step-by-step explanation:
To find the area and perimeter of a rectangle, we first need to calculate its length and width. Since the four vertices of the rectangle are given as (-2,-7), (5,-7), (5,1), and (-2,1), we can easily calculate that the length of the rectangle is the difference between the x-coordinates 5 and -2, which is 7, and the width is the difference between the y-coordinates 1 and -7, which is 8.
Once we have the length and width, the area of a rectangle is calculated by the formula Area = length x width. Thus, Area = 7 x 8 = 56 square units.
To find the perimeter, we use the formula Perimeter = 2(length + width). Thus, Perimeter = 2(7 + 8) = 30 units.
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