To calculate the area of the five rectangular lateral faces of a rectangular prism (a box), we first need to understand the dimensions given: 5, 6, and 4. Let's assume these represent the length (l), width (w), and height (h) of the prism.
The area of the lateral faces consists of the areas of the four rectangular sides that are not the top and bottom faces. For a rectangular prism, the lateral faces consist of the following pairs:
- Two faces with dimensions \(h \times w\)
- Two faces with dimensions \(h \times l\)
- Two faces with dimensions \(w \times l\) (but these are the top and bottom faces, which we don't consider in the lateral area)
Given:
- Length (l) = 6
- Width (w) = 5
- Height (h) = 4
Now, we calculate the areas of the lateral faces:
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Area of the two \(h \times w\) faces: \[ 2 \times (h \times w) = 2 \times (4 \times 5) = 2 \times 20 = 40 \]
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Area of the two \(h \times l\) faces: \[ 2 \times (h \times l) = 2 \times (4 \times 6) = 2 \times 24 = 48 \]
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Area of the two \(w \times l\) faces (not relevant for lateral area since they are top and bottom): \[ 0 \]
Now, we add the areas of the two sets of lateral faces together: \[ \text{Total Lateral Area} = 40 + 48 = 88 \]
Therefore, the total area of the five rectangular lateral faces is \( \boxed{88} \).