To find the area of the polygon described, we can break it down into parts: the two pillars, the triangular roof, the door, and the chimney.
1. Area of the Pillars:
- Each pillar is a rectangle with a length of 4 and a width of 3.
- Area of one pillar = length × width = 4 × 3 = 12 square units.
- Since there are two pillars, total area for both = 12 × 2 = 24 square units.
2. Area of the Door:
- The door, located between the two pillars, has a width of 2 and an inner height of 3.5.
- Area of the door = width × height = 2 × 3.5 = 7 square units.
3. Area of the Triangular Roof:
- The triangular roof has a base that extends to the outer edges of the pillars and a height of 6.
- The base of the triangle spans the outer edges of the pillars plus the sides extending outward: 3 (width of the left pillar) + 2 (door width) + 3 (width of the right pillar) = 8 units.
- The base is actually the combined width of the two pillars (6) plus the extra extending parts (2) for a total width of 8 units.
- Area of the triangle = 0.5 × base × height = 0.5 × 8 × 6 = 24 square units.
4. Area of the Chimney:
- The chimney is also a rectangle. Its width is given as 1, and height is given as 2. However, since it is sitting on the roof and has a thickness of 1, the area is simply its face area.
- Area of the chimney = width × height = 1 × 2 = 2 square units.
Total Area Calculation:
- Total area = Area of pillars + Area of door + Area of triangular roof + Area of chimney.
- Total area = 24 + 7 + 24 + 2 = 57 square units.
Based on the description and calculations, none of the listed responses provide a correct area of 57 square units. It is important to double-check to ensure all dimensions and assumptions used in the area calculations are accurate. Please check if any aspect might have been interpreted differently based on the image you mentioned or look for any additional parts I may have missed in the polygon that adds to its area.