How to Find the Area of a Polygon with Given Vertices?

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 (x_iy_i+1) – Σ (y_ix_i+1) |

Calculating the sums:

• First sum (x_iy_i+1):
• 1 * 3 = 3
• 7 * 7 = 49
• 7 * 7 = 49
• 4 * 3 = 12
• Total = 3 + 49 + 49 + 12 = 113

• Second sum (y_ix_i+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.