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
To find the total surface area of the figure, we need to find the surface area of each individual rectangular prism and then add them together.
1. Surface Area of the larger rectangular prism:
- Front and back faces: 12 cm * 18 cm = 216 cm^2 * 2 = 432 cm^2
- Top and bottom faces: 12 cm * 4 cm = 48 cm^2 * 2 = 96 cm^2
- Right and left faces: 18 cm * 4 cm = 72 cm^2 * 2 = 144 cm^2
Total surface area of the larger rectangular prism: 432 cm^2 + 96 cm^2 + 144 cm^2 = 672 cm^2
2. Surface Area of each smaller rectangular prism (step):
- Front and back faces: 4 cm * 6 cm = 24 cm^2 * 2 = 48 cm^2
- Top and bottom faces: 4 cm * 4 cm = 16 cm^2 * 2 = 32 cm^2
- Right and left faces: 6 cm * 4 cm = 24 cm^2 * 2 = 48 cm^2
Total surface area of each smaller rectangular prism: 48 cm^2 + 32 cm^2 + 48 cm^2 = 128 cm^2
To find the total surface area of the figure, we add the surface area of the larger rectangular prism to the combined surface area of the three smaller rectangular prisms:
672 cm^2 + (128 cm^2 * 3) = 672 cm^2 + 384 cm^2 = 1056 cm^2
Therefore, the total surface area of the figure is 1056 square centimeters.