To find the area of the polygon, we need to find the area of each individual shape (rectangle, triangle, and trapezoid) and then add them together.
Area of the rectangular pillars: 4 * 3 = 12 each side, total = 24 square units
Area of the door: 2 * 3.5 = 7 square units
Area of the triangular roof: 0.5 * 2 * 6 = 6 square units
Area of the chimney: (1 + 2) * 1 * 0.5 = 1.5 square units
Total area: 24 (rectangular pillars) + 7 (door) + 6 (triangular roof) + 1.5 (chimney) = 61.5 square units
Therefore, the area of the polygon is 61.5 square units. The answer is 61.5 square units.