Answer:
2520 m²
Explanation:
You want the surface area of the irregular prism shown.
Perimeter
The perimeter of the base (shaded front face) is the sum of the lengths of the horizontal edges and the lengths of the vertical edges. That sum is ...
2(20 m) +2(20 m) = 80 m
Lateral area
The lateral area of the prism is the sum of the unshaded rectangle areas. That total area is the product of the perimeter of the base and the distance between bases:
LA = Ph = (80 m)(25 m) = 2000 m²
Base area
The area of each of the two bases can be found several ways. We find the height of the middle step to be (20 m -7 m -6 m) = 7 m, so the bottom step fits nicely into the space not used by the middle step. (This is shown in the attachment.)
That is, the base area can be computed as the area of a rectangle 13 m high and 20 m wide:
Base area = WH = (20 m)(13 m) = 260 m²
Surface area
The total surface area of the prism is the sum of the lateral area and the area of the two bases:
SA = LA +2·B = (2000 m²) +2(260 m²) = 2520 m²
The surface area of the prism is 2520 square meters.