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)
Responses
444 cm2
444 cm squared
480 cm2
480 cm squared
552 cm2
552 cm squared
408 cm2
To find the total surface area of the figure, we need to calculate the surface area of each face of the composite figure and add them together.
The visible faces are:
- Top face: 3 steps of 4 cm x 18 cm = 72 cm2
- Side face: (12 cm x 18 cm) + (2 cm x 18 cm) = 216 cm2
- Front face: (12 cm x 2 cm) + (12 cm x 6 cm) + (12 cm x 6 cm) = 120 cm2
Adding these together:
72 cm2 + 216 cm2 + 120 cm2 = 408 cm2
Therefore, the total surface area of the figure is 408 cm2.
Answer: 408 cm2