Short Answer 
To find the area of a pentagon using the Shoelace Formula, first list its vertices in order. Calculate the sums of the products of coordinates as specified, resulting in values of -12 and 12, then use these to find the area, which is 12 square units.
Step 1: List the Coordinates
Begin by organizing the vertices of the polygon in either a clockwise or counterclockwise sequence. This step is crucial for accurately applying the Shoelace Formula. The vertices for this pentagon are:
- (-4, 0)
- (0, 4)
- (2, 2)
- (1, 2)
- (1, 0)
Step 2: Calculate Products of Coordinates
Next, compute the sums based on the ordered coordinates. First, find the sum of the products of the x-coordinates with the y-coordinates of the next vertex:
- -4 * 4 = -16
- 0 * 2 = 0
- 2 * 2 = 4
- 1 * 0 = 0
- 1 * 0 = 0
So, the total is: -16 + 0 + 4 + 0 + 0 = -12.
Step 3: Apply the Shoelace Formula
Now, calculate the second sum where the y-coordinates are multiplied with the x-coordinates of the next vertex:
- 0 * 0 = 0
- 4 * 2 = 8
- 2 * 1 = 2
- 2 * 1 = 2
- 0 * -4 = 0
This results in a total of 0 + 8 + 2 + 2 + 0 = 12. Subtract this from the first sum, take the absolute value, and divide by 2 to find the area:
Area = 0.5 * |-12 – 12| = 0.5 * |-24| = 0.5 * 24 = 12 square units.