To find the area of a polygon given its vertices, we can use the shoelace formula. In this case, the vertices of the polygon are at the following coordinates: (1, 3), (7, 3), (7, 7), and (4, 7).
First, we’ll list the coordinates in order:
- (1, 3)
- (7, 3)
- (7, 7)
- (4, 7)
- (1, 3)
Now, we apply the shoelace formula:
Area = 0.5 × | Σ (xiyi+1) – Σ (yixi+1) |
Calculating the sums:
- First sum (xiyi+1):
- 1 * 3 = 3
- 7 * 7 = 49
- 7 * 7 = 49
- 4 * 3 = 12
- Total = 3 + 49 + 49 + 12 = 113
- Second sum (yixi+1):
- 3 * 7 = 21
- 3 * 7 = 21
- 7 * 4 = 28
- 7 * 1 = 7
- Total = 21 + 21 + 28 + 7 = 77
Putting this into the shoelace formula:
Area = 0.5 × | 113 – 77 | = 0.5 × 36 = 18
Thus, the area of the polygon with the given vertices is 18 square units.