To find the total surface area of the figure, we need to calculate the surface area of each individual step and the remaining portion of the rectangular prism.
Surface area of one step:
- Top face: 4 cm x 2 cm = 8 cm^2
- Front face: 6 cm x 2 cm = 12 cm^2
- Side face: 6 cm x 4 cm = 24 cm^2
Total surface area of one step = 8 cm^2 + 12 cm^2 + 24 cm^2 = 44 cm^2
Since there are three steps, the total surface area of the steps is 3 x 44 cm^2 = 132 cm^2
Remaining portion of the rectangular prism (bottom, back, left side, and bottom side):
- Bottom face: 12 cm x 2 cm = 24 cm^2
- Back face: 18 cm x 2 cm = 36 cm^2
- Left side face: 18 cm x 4 cm = 72 cm^2
- Bottom side face: 12 cm x 18 cm = 216 cm^2
Total surface area of the remaining portion = 24 cm^2 + 36 cm^2 + 72 cm^2 + 216 cm^2 = 348 cm^2
Total surface area of the figure = total surface area of steps + surface area of remaining portion
= 132 cm^2 + 348 cm^2
= 480 cm^2
Therefore, the total surface area of the figure is 480 cm^2.
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?(1 point)Responses480 cm2
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