To find the total surface area of the figure, we need to calculate the surface area of each individual rectangular prism and add them together.
Surface area of the rectangular prism with dimensions 12 cm x 2 cm x 18 cm:
2(12 x 2) + 2(12 x 18) + 2(2 x 18) = 48 + 432 + 72 = 552 cm²
Surface area of the two rectangular prisms that make up the steps:
2(4 x 2) + 2(4 x 6) + 2(2 x 6) = 16 + 48 + 24 = 88 cm²
Total surface area of the figure:
552 cm² + 88 cm² = 640 cm²
Therefore, the total surface area of the figure is 640 cm².
se 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
480 cm2
480 cm squared
444 cm2 444 cm squared
552 cm2
552 cm squared
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3 answers
out of the options
Actually, my previous calculations were incorrect. Let's correct it based on the information given in the image:
The surface area of the rectangular prism with dimensions 12 cm x 2 cm x 18 cm:
2(12 x 2) + 2(12 x 18) + 2(2 x 18) = 24 + 432 + 72 = 528 cm²
The surface area of the two rectangular prisms that make up the steps:
2(4 x 2) + 2(4 x 6) + 2(2 x 6) = 16 + 48 + 24 = 88 cm²
Adding them together:
528 cm² + 88 cm² = 616 cm²
So, the correct answer from the options provided is:
552 cm²
The surface area of the rectangular prism with dimensions 12 cm x 2 cm x 18 cm:
2(12 x 2) + 2(12 x 18) + 2(2 x 18) = 24 + 432 + 72 = 528 cm²
The surface area of the two rectangular prisms that make up the steps:
2(4 x 2) + 2(4 x 6) + 2(2 x 6) = 16 + 48 + 24 = 88 cm²
Adding them together:
528 cm² + 88 cm² = 616 cm²
So, the correct answer from the options provided is:
552 cm²