To determine the total surface area of the three-dimensional figure based on the provided measurements, we need to calculate the area of each individual face and then sum them up.
Given dimensions:
- Back: 17 cm
- Left Side: 4 cm
- Bottom: 10 cm
Step 1: Calculate the areas of each face
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Area of the Back: The back is a rectangle, so we can calculate the area using the formula: \[ \text{Area} = \text{length} \times \text{height} \] Assuming the Back has a length of 17 cm and a width (which might be equivalent to the Left Side height, depending on the shape) of 10 cm: \[ \text{Area of the Back} = 17 , \text{cm} \times 10 , \text{cm} = 170 , \text{cm}^2 \]
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Area of the Left Side: The left side is also a rectangle. Assuming the height is 4 cm and width as another dimension of 10 cm: \[ \text{Area of the Left Side} = 4 , \text{cm} \times 10 , \text{cm} = 40 , \text{cm}^2 \]
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Area of the Bottom: The bottom is a rectangle as well. Assuming dimensions as 17 cm (length) and 10 cm (width): \[ \text{Area of the Bottom} = 17 , \text{cm} \times 10 , \text{cm} = 170 , \text{cm}^2 \]
Step 2: Sum the areas to find the total surface area
Now, we sum the areas of all the sides to get the total surface area: \[ \text{Total Surface Area} = \text{Area of the Back} + \text{Area of the Left Side} + \text{Area of the Bottom} \] Assuming these are the only sides measured, the total surface area calculation will need to include any additional sides remaining.
Calculated Areas:
- Area of the Back: 170 cm²
- Area of the Left Side: 40 cm²
- Area of the Bottom: 170 cm²
Thus: \[ \text{TOTAL Surface Area} = 170 + 40 + 170 = 380 , \text{cm}^2 \]
Final Answers:
- Area of the Left Side = 40 cm²
- Area of the Back = 170 cm²
- Area of the Bottom = 170 cm²
- TOTAL Surface Area of the figure = 380 cm²