To find the total surface area of the figure, we need to calculate the surface area of the rectangular prism and the surface area of the missing section separately, then subtract the surface area of the missing section from the surface area of the rectangular prism.
Surface area of the rectangular prism:
- Front face: 13.7 cm * 11.5 cm = 157.55 cm²
- Back face: 13.7 cm * 11.5 cm = 157.55 cm²
- Top face: 13.7 cm * 6.2 cm = 84.94 cm²
- Bottom face: 13.7 cm * 6.2 cm = 84.94 cm²
- Left face: 11.5 cm * 6.2 cm = 71.30 cm²
- Right face: 11.5 cm * 6.2 cm = 71.30 cm²
Surface area of the rectangular prism = 2(157.55 cm²) + 2(84.94 cm²) + 2(71.30 cm²) = 617.58 cm²
Surface area of the missing section:
- Front face: 7.5 cm * 7.5 cm = 56.25 cm²
- Top face: 7.5 cm * 3 cm = 22.5 cm²
- Right face: 7.5 cm * 3 cm = 22.5 cm²
- Left face: 7.5 cm * 6.2 cm = 46.5 cm²
Surface area of the missing section = 56.25 cm² + 22.5 cm² + 22.5 cm² + 46.5 cm² = 147.75 cm²
Total surface area of the figure = Surface area of the rectangular prism - Surface area of the missing section
Total surface area = 617.58 cm² - 147.75 cm² = 469.83 cm²
So, the total surface area of the figure is approximately 469.83 cm². None of the provided answer options match this calculation, so it seems there may be an error in the options given.
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
53.4 cm2
353.8 cm2
377.8 cm2
365.8 cm2
1 answer