To find the total surface area of the composite figure made up of the two rectangular prisms, we will calculate the surface area of each prism separately and then account for the areas that are not exposed.
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Rectangular Prism on the Left:
- Length (L) = 10 mm
- Height (H) = 8 mm
- Width (W): We can find W since the total length (L1 + L2) = 16 mm and the length of the right prism (L2) is 6 mm, thus: \( W = 16 mm - 10 mm = 6 mm \).
- The dimensions of the left prism are therefore: \( L = 10 \) mm, \( W = 6 \) mm, \( H = 8 \) mm.
The surface area \( A \) of a rectangular prism is calculated by the formula: \[ A = 2(LW + LH + WH) \] Plugging in the values: \[ A_{left} = 2(10 \times 6 + 10 \times 8 + 6 \times 8) \] \[ = 2(60 + 80 + 48) = 2(188) = 376 \text{ mm}^2 \]
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Rectangular Prism on the Right:
- Length (L) = 6 mm
- Width (W) = 6 mm
- Height (H) = 6 mm
Using the surface area formula again: \[ A_{right} = 2(6 \times 6 + 6 \times 6 + 6 \times 6) \] \[ = 2(36 + 36 + 36) = 2(108) = 216 \text{ mm}^2 \]
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Subtracting the Overlap: Since the two prisms are combined, the area of the face where they join (the front face of the left prism that overlaps with the right prism) is counted twice. This face has dimensions:
- Height = 6 mm (matching the right prism)
- Width = 6 mm
The area of this face is: \[ A_{overlap} = H \times W = 6 \times 6 = 36 \text{ mm}^2 \]
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Total Surface Area Calculation: Combine the surface areas of both prisms and subtract the overlapping area: \[ A_{total} = A_{left} + A_{right} - A_{overlap} \] \[ = 376 + 216 - 36 = 556 \text{ mm}^2 \]
Therefore, the total surface area of the figure is \( \boxed{556} \) mm\(^2\).