Final answer:
The given figure is a rectangle. The perimeter of the rectangle is 42 units and the area is 104 square units. Adding a 2 unit walkway increases the perimeter to 58 units. If each unit represents 3.5 feet, then the figure would require 16.57 yards of fencing.
Step-by-step explanation:
To calculate the perimeter and area of the given figure, we need to first plot the points on the graph paper.
Plotting the 4 points A(2,5), B(2,-8), C(6,-8), D(6,5) on the graph paper, we can see that they form a rectangle.
To calculate the perimeter of the rectangle, we sum up the lengths of all four sides.
The length of AB is 13, BC is 8, CD is 13, and DA is 8, resulting in a total perimeter of 42 units.
To calculate the area of the rectangle, we multiply the length of one side by the length of an adjacent side.
The length of AB is 13 and the adjacent side BC is 8, so the area of the rectangle is 104 square units.
Next, if we place a 2 unit walkway all the way around the figure, we need to increase the length and width of the rectangle by 4 units (2 units for each side).
The new dimensions of the rectangle would be AB = 17, BC = 12, CD = 17, and DA = 12.
Therefore, the perimeter of the rectangle with the walkway is 58 units.
If each unit on the graph paper is equivalent to 3.5 feet, then to find the number of yards of fencing needed to enclose the figure, we divide the total perimeter (58) by the conversion factor (3.5) to get 16.57 yards.