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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

365.8 cm2 365.8 cm squared

353.8 cm2
353.8 cm squared

377.8 cm2
377.8 cm squared

53.4 cm2
53.4 cm squared
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Answer 1

To solve for the total surface area of the figure, we first need to find the surface area of the rectangular prism with the missing section, then subtract the surface area of the missing section to get the total surface area.

Surface area of the rectangular prism:
- Front face: 13.7 cm * 11.5 cm = 157.55 cm²
- Top face: 13.7 cm * 6.2 cm = 84.94 cm²
- Right face: 11.5 cm * 4 cm = 46 cm²
- Bottom face: 13.7 cm * 11.5 cm = 157.55 cm²
- Left face: 11.5 cm * 6.2 cm = 71.3 cm²
- Back face: 11.5 cm * 6.2 cm = 71.3 cm²

Total surface area of the rectangular prism: 157.55 + 84.94 + 46 + 157.55 + 71.3 + 71.3 = 588.64 cm²

Surface area of the missing section:
- Front face: 3 cm * 7.5 cm = 22.5 cm²
- Top face: 7.5 cm * 6.2 cm = 46.5 cm²
- Right face: 3 cm * 4 cm = 12 cm²
- Bottom face: 7.5 cm * 3 cm = 22.5 cm²
- Left face: 4 cm * 6.2 cm = 24.8 cm²
- Back face: 4 cm * 6.2 cm = 24.8 cm²

Total surface area of the missing section: 22.5 + 46.5 + 12 + 22.5 + 24.8 + 24.8 = 153.1 cm²

Total surface area of the figure: 588.64 cm² - 153.1 cm² = 435.54 cm²

Therefore, the total surface area of the figure is 435.54 cm².