To determine the total surface area of a three-dimensional figure, we need to know its shape, the dimensions, and how many faces it has. Unfortunately, the figure isn't provided in your prompt, so I will guide you through the typical steps you would take to calculate the total surface area, assuming it's a standard shape like a rectangular prism.
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Identify the faces: A rectangular prism has 6 faces (front, back, left, right, top, bottom).
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Calculate the area of each face:
- Area of the Left Side: Typically calculated as height × depth.
- Area of the Back: Typically calculated as width × height.
- Area of the Bottom: Typically calculated as width × depth.
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Total Surface Area Calculation: The total surface area (SA) of a rectangular prism can be computed as: \[ SA = 2 \times (l \times w + l \times h + w \times h) \] where \(l\) is length, \(w\) is width, and \(h\) is height.
To answer your questions and fill in the blanks from your prompt:
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How many faces does this shape have?
- If it is a rectangular prism, the answer would be 6 faces.
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Area of the Left Side =
- Calculate using dimensions specific to the left side (e.g., if height = 4 in, depth = 3 in, then Area = 4 * 3 = 12 square inches).
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Area of the Back =
- Similarly, calculate using dimensions specific to the back (e.g., if width = 5 in, height = 4 in, then Area = 5 * 4 = 20 square inches).
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Area of the Bottom =
- Calculate using dimensions specific to the bottom (e.g., if width = 5 in, depth = 3 in, then Area = 5 * 3 = 15 square inches).
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TOTAL surface area of the figure =
- You would sum all the face areas calculated: \[ SA = (Area , of , Left + Area , of , Back + Area , of , Bottom + Area , of , Right + Area , of , Front + Area , of , Top) \]
Insert the calculated areas into the blank fields, and verify the total matches the dimensions of your specific three-dimensional figure.
If you can provide the dimensions or the specific shape of the figure, I would be happy to assist with those calculations more accurately!