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
480 cm2
480 cm squared
552 cm2
552 cm squared
408 cm2
408 cm squared
444 cm2
The total surface area of the figure can be found by calculating the surface area of each individual rectangular prism and then adding them together.
Surface area of the larger rectangular prism:
2(12*2) + 2(12*18) + 2(2*18) = 48 + 432 + 72 = 552 cm2
Surface area of the two smaller rectangular prisms:
2(4*2) + 2(4*6) + 2(2*6) = 16 + 48 + 24 = 88 cm2
Total surface area = surface area of larger rectangular prism - surface area of two smaller rectangular prisms
552 cm2 - 88 cm2 = 464 cm2
Therefore, the total surface area of the figure is 464 cm2.