To calculate the surface area of the L-shaped platform that Nikolai is making, we first need to determine the area of the L-shape.
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Dimensions of the entire rectangle:
- Length = 16 inches
- Width = 10 inches
Therefore, the area of the entire rectangle is: \[ \text{Area}_{\text{total}} = \text{Length} \times \text{Width} = 16 , \text{in} \times 10 , \text{in} = 160 , \text{in}^2 \]
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Dimensions of the removed portion:
- Length of the removed portion = 12 inches
- Width of the removed portion = 4 inches (since the shorter portion has a width of 4 inches)
Therefore, the area of the removed rectangle is: \[ \text{Area}{\text{removed}} = \text{Length}{\text{removed}} \times \text{Width}_{\text{removed}} = 12 , \text{in} \times 4 , \text{in} = 48 , \text{in}^2 \]
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Calculating the area of the L-shape (after removing the rectangle): \[ \text{Area}{\text{L-shape}} = \text{Area}{\text{total}} - \text{Area}_{\text{removed}} = 160 , \text{in}^2 - 48 , \text{in}^2 = 112 , \text{in}^2 \]
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Calculating the surface area of the platform (which is 3 inches thick): Since the surface area is technically also influenced by thickness, and assuming we want the area for the sides as well, we typically just consider the surface area of the top face in this case.
However, since the platform is just the top face, we will calculate as follows: \[ \text{Surface Area}{\text{platform}} = \text{Area}{\text{L-shape}} = 112 , \text{in}^2 \]
Thus, the final answer for the surface area of the platform (top face) is: \[ \boxed{112} , \text{in}^2 \]