Surface Area of Composite 3D Figures Quick Check
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Question
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 also in the shape of a rectangular prism. The top, right, and front faces of the figure are visible. "The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 13.7 centimeters and a height of 11.5 centimeters. The missing section is removed from the bottom right corner of the rectangular prism. The missing section is a rectangular prism that shares a width of 3 centimeters with the rest of the figure. The missing rectangular prism section has a length of 7.5 centimeters and a height of 7.5 centimeters. The remaining length to the left of the missing section both measures 6.2 centimeters. The remaining height above the missing section measures 4 centimeters.
Solve for the total surface area of the figure.
(1 point)
Responses
353.8 cm2
353.8 cm squared
365.8 cm2 365.8 cm squared
53.4 cm2
53.4 cm squared
377.8 cm2
377.8 cm squared
To solve for the total surface area of the figure, we need to calculate the surface area of each individual rectangular prism and then subtract the surface area of the missing section.
First, calculate the surface area of the rectangular prism:
- Front and back faces: 13.7 cm * 11.5 cm * 2 = 314.9 cm²
- Top and bottom faces: 13.7 cm * 6.2 cm * 2 = 169.3 cm²
- Left and right faces: 11.5 cm * 6.2 cm * 2 = 142.3 cm²
Total surface area of the rectangular prism = 314.9 cm² + 169.3 cm² + 142.3 cm² = 626.5 cm²
Next, calculate the surface area of the missing rectangular prism section (bottom right corner):
- Front and back faces: 7.5 cm * 7.5 cm * 2 = 112.5 cm²
- Top and bottom faces: 7.5 cm * 3 cm * 2 = 45 cm²
- Left and right faces: 3 cm * 7.5 cm * 2 = 45 cm²
Total surface area of the missing section = 112.5 cm² + 45 cm² + 45 cm² = 202.5 cm²
Finally, subtract the surface area of the missing section from the total surface area of the rectangular prism:
Total surface area = 626.5 cm² - 202.5 cm² = 424 cm²
Therefore, the total surface area of the figure is 424 cm². None of the provided responses match this answer.
no, the correct answers are
353.8 cm2
408 cm2
1,171.5 in.2
330 ft.2
222 in.2