To find the total surface area of a rectangular prism, we use the formula:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.
From the information you provided, we have dimensions as follows:
- The top measurement (Box 1) indicates the length \( l = 4 \) cm.
- The left side (Box 2) has two dimensions given: \( w = 6 \) cm and \( h = 4 \) cm. Here, we need to interpret which represents width and height.
Since typically we will consider the left side to be the height, we can assign:
- \( h = 6 \) cm (height from Box 2).
- Then, from Box 3 (the bottom), we have \( w = 9 \) cm.
Now let’s clarify the dimensions again as:
- Length (\( l \)): 4 cm
- Width (\( w \)): 9 cm
- Height (\( h \)): 6 cm
Now we can substitute these values into the surface area formula:
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Calculate \( lw \): \[ lw = 4 \times 9 = 36 \]
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Calculate \( lh \): \[ lh = 4 \times 6 = 24 \]
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Calculate \( wh \): \[ wh = 9 \times 6 = 54 \]
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Sum these areas: \[ lw + lh + wh = 36 + 24 + 54 = 114 \]
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Finally, calculate the total surface area: \[ \text{Surface Area} = 2 \times 114 = 228 \text{ square centimeters} \]
Thus, the total surface area of the rectangular prism is \(\boxed{228}\) square centimeters.