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The shape is made of a cube and a rectangular prism with a square base. Complete the table below to find its surface area.
area of the partial face
area of the rest of the cube
area of the rectangular prism without the hidden face
total surface area
578 in.²
500 in.²
70 in.²
678 in.²
100 in.²
To find the total surface area of the shape comprising a cube and a rectangular prism, we need to analyze the provided areas step-by-step.
1. Area of the partial face: Given as 578 in².
2. Area of the rest of the cube: Given as 500 in².
3. Area of the rectangular prism without the hidden face: Given as 70 in².
The total surface area can be calculated by adding the areas of the visible parts of both shapes:
[
text{Total Surface Area} = text{Area of Partial Face} + text{Area of Cube} + text{Area of Rectangular Prism}
]
However, there’s more to consider since this looks like a composite shape. The total provided areas (578 in² + 500 in² + 70 in²) would typically face adjustments for overlaps or hidden faces, but since only exposed areas are given, we can use the total directly.
– Total Surface Area: 678 in² given as an option.
Thus, you can conclude that if these areas are correct and account for overlaps or hidden faces, the calculations align.
Your final total surface area of the shape should be 678 in² as provided. If you have more questions or need further clarifications on any part of the process, feel free to ask!