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
377.8 cm2
377.8 cm squared
365.8 cm2 365.8 cm squared
353.8 cm2
353.8 cm squared
53.4 cm2
53.4 cm squared
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To solve for the total surface area of the figure, we need to find the surface area of each individual face and then add them all together.
1. Surface Area of the top face of the rectangular prism:
- 13.7 cm * 11.5 cm = 157.55 cm2
2. Surface Area of the front face of the rectangular prism:
- 13.7 cm * 4 cm = 54.8 cm2
3. Surface Area of the right face of the rectangular prism:
- 11.5 cm * 4 cm = 46 cm2
4. Surface Area of the missing section (rectangle removed):
- 7.5 cm * 3 cm = 22.5 cm2
Now, let's calculate the total surface area:
- Total Surface Area = 2 * (top face area + front face area + right face area) - area of the missing section
- Total Surface Area = 2 * (157.55 cm2 + 54.8 cm2 + 46 cm2) - 22.5 cm2
- Total Surface Area = 2 * 258.35 cm2 - 22.5 cm2
- Total Surface Area = 516.7 cm2 - 22.5 cm2
- Total Surface Area = 494.2 cm2
Therefore, the total surface area of the figure is 494.2 cm2.