To determine the total surface area of the given three-dimensional figure, we need to first find the area of each specified side: the left side, the back, and the bottom.
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Area of the Left Side: The left side is typically a rectangle. Assuming the left side has a height of 17 cm and a width that corresponds to the bottom dimension (10 cm): \[ \text{Area of the Left Side} = \text{Height} \times \text{Width} = 17 , \text{cm} \times 10 , \text{cm} = 170 , \text{cm}^2 \]
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Area of the Back: The back side is also a rectangle. Assuming the back has a height of 17 cm and a depth that corresponds to the depth (or back dimension) of 4 cm: \[ \text{Area of the Back} = \text{Height} \times \text{Depth} = 17 , \text{cm} \times 4 , \text{cm} = 68 , \text{cm}^2 \]
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Area of the Bottom: The bottom is a rectangle as well, corresponding to the bottom dimensions of the figure (width of 10 cm and depth of 4 cm): \[ \text{Area of the Bottom} = \text{Width} \times \text{Depth} = 10 , \text{cm} \times 4 , \text{cm} = 40 , \text{cm}^2 \]
Now, we can sum the areas of these three sides to find the total surface area of the figure (since the figure appears to have only these three sides exposed):
\[ \text{TOTAL Surface Area} = \text{Area of the Left Side} + \text{Area of the Back} + \text{Area of the Bottom} = 170 , \text{cm}^2 + 68 , \text{cm}^2 + 40 , \text{cm}^2 \] \[ \text{TOTAL Surface Area} = 278 , \text{cm}^2 \]
Summary:
- Area of the Left Side = \(170 , \text{cm}^2\)
- Area of the Back = \(68 , \text{cm}^2\)
- Area of the Bottom = \(40 , \text{cm}^2\)
- TOTAL surface area of the figure = \(278 , \text{cm}^2\)