Use the image to answer the question.
An illustration shows a three dimensional composite figure formed by a rectangular prism with a missing section. The missing section is in the shape of two rectangular prisms. With the section removed, the figure resembles three steps. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 12 centimeters at the bottom, a width of 2 centimeters, and a height of 18 centimeters. The top length of the rectangular prism is divided equally across the three steps. Each step has a length of 4 centimeters. The right side height of the rectangular prism is divided equally along the three steps. Each step has a height of 6 centimeters.
What is the total surface area of the figure?
To find the total surface area of the figure, we need to calculate the surface area of each individual shape and then add them together.
1. Surface area of the rectangular prism:
- Front and back faces: 12 cm * 18 cm * 2 = 432 cm^2
- Top and bottom faces: 12 cm * 2 cm * 2 = 48 cm^2
- Left and right faces: 18 cm * 2 cm * 2 = 72 cm^2
Total surface area of rectangular prism = 432 + 48 + 72 = 552 cm^2
2. Surface area of the three steps:
- Front and back faces: 4 cm * 18 cm * 2 = 144 cm^2 (for each step, total for all 3 steps = 144 * 3 = 432 cm^2)
- Top and bottom faces: 4 cm * 2 cm * 2 = 16 cm^2 (for each step, total for all 3 steps = 16 * 3 = 48 cm^2)
- Left and right faces: 6 cm * 2 cm * 2 = 24 cm^2 (for each step, total for all 3 steps = 24 * 3 = 72 cm^2)
Total surface area of the three steps = 432 + 48 + 72 = 552 cm^2
Therefore, the total surface area of the figure is 552 cm^2 (rectangular prism) + 552 cm^2 (three steps) = 1104 cm^2.