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?
480 cm2
444 cm2
408 cm2
552 cm2
To find the total surface area of the figure, we need to find the surface area of each individual rectangular prism and then subtract the surface area of the missing section and add the surface area of the steps.
The surface area of the larger rectangular prism:
- Front and back faces: 2 (12 cm x 18 cm) = 2 x 216 cm2 = 432 cm2
- Top and bottom faces: 2 (12 cm x 2 cm) = 2 x 24 cm2 = 48 cm2
- Left and right faces: 2 (18 cm x 2 cm) = 2 x 36 cm2 = 72 cm2
Total surface area of the larger rectangular prism = 432 cm2 + 48 cm2 + 72 cm2 = 552 cm2
The missing section is made up of two smaller rectangular prisms:
- Surface area of each smaller rectangular prism = 2 (4 cm x 6 cm + 4 cm x 2 cm + 6 cm x 2 cm) = 2 (24 cm2 + 8 cm2 + 12 cm2) = 2 x 44 cm2 = 88 cm2
Total surface area of the missing section = 88 cm2 + 88 cm2 = 176 cm2
The surface area of the three steps:
- Front and back faces: 2 (4 cm x 18 cm + 4 cm x 12 cm + 4 cm x 6 cm) = 2 (72 cm2 + 48 cm2 + 24 cm2) = 2 x 144 cm2 = 288 cm2
- Top and bottom faces: 2 (4 cm x 2 cm + 4 cm x 2 cm + 4 cm x 2 cm) = 2 (8 cm2 + 8 cm2 + 8 cm2) = 2 x 24 cm2 = 48 cm2
- Left and right faces: 2 (18 cm x 6 cm + 12 cm x 6 cm + 6 cm x 6 cm) = 2 (108 cm2 + 72 cm2 + 36 cm2) = 2 x 216 cm2 = 432 cm2
Total surface area of the three steps = 288 cm2 + 48 cm2 + 432 cm2 = 768 cm2
Total surface area = 552 cm2 - 176 cm2 + 768 cm2 = 1144 cm2
The total surface area of the figure is 1144 cm2. None of the provided answer choices matches this calculation.