To find the total surface area of the figure, you first need to find the surface area of each individual part (rectangular prism and the two rectangular prisms that form the missing section) and then add them all together.
Surface area of rectangular prism:
- Front and back face: 12 cm x 18 cm = 216 cm^2 (double it for both front and back)
- Top and bottom face: 12 cm x 2 cm = 24 cm^2 (double it for both top and bottom)
- Side faces: 18 cm x 2 cm = 36 cm^2 (double it for both sides)
Total surface area of rectangular prism: 2(216) + 2(24) + 2(36) = 432 + 48 + 72 = 552 cm^2
Surface area of missing section (two rectangular prisms):
- Front and back face: 4 cm x 6 cm = 24 cm^2 (double it for both front and back)
- Top and bottom face: 4 cm x 2 cm = 8 cm^2 (double it for both top and bottom)
- Side faces: 6 cm x 2 cm = 12 cm^2 (double it for both sides)
Total surface area of missing section: 2(24) + 2(8) + 2(12) = 48 + 16 + 24 = 88 cm^2
Total surface area of the figure: Surface area of rectangular prism + Surface area of missing section
552 cm^2 + 88 cm^2 = 640 cm^2
Therefore, the total surface area of the figure is 640 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)
Responses
408 cm2
408 cm squared
552 cm2
552 cm squared
444 cm2 444 cm squared
480 cm2
480 cm squared
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3 answers
pick one of my answers that are correct
552 cm2 or 552 cm squared
1 answer