To find the total surface area of the composite figure formed by the two rectangular prisms, we need to calculate the surface area of each prism separately and then combine them, subtracting the area of the overlapping face where they connect.
Step 1: Identify Dimensions
-
Left rectangular prism:
- Length \( L_1 = 10 \) mm
- Height \( H_1 = 8 \) mm
- Width \( W_1 \) is unknown but can be inferred.
Given that the total length of both prisms is 16 mm and the right prism's length is 6 mm, we can find the width \( W_1 \). Since the width of the left prism aligns with the width of the right prism, we need the dimensions of the right prism.
-
Right rectangular prism:
- Length \( L_2 = 6 \) mm
- Width \( W_2 = 6 \) mm
- Height \( H_2 = 6 \) mm
Step 2: Calculate the Surface Area of Each Prism
Surface area formula for a rectangular prism: \[ \text{Surface Area} = 2(LW + LH + WH) \]
Surface Area of the Left Prism:
- Assume width \( W_1 = W_2 = 6 \) mm (aligns with the right prism).
- Then:
- Surface area of left prism: \[ \text{Surface Area}_1 = 2(10 \times 6 + 10 \times 8 + 6 \times 8) \] \[ = 2(60 + 80 + 48) = 2(188) = 376 \text{ mm}^2 \]
Surface Area of the Right Prism:
- Surface area of right prism: \[ \text{Surface Area}_2 = 2(6 \times 6 + 6 \times 6 + 6 \times 6) \] \[ = 2(36 + 36 + 36) = 2(108) = 216 \text{ mm}^2 \]
Step 3: Subtract the Overlapping Area
Since the left and right prisms are joined, the area of the overlapping face must be subtracted.
- Area of the overlapping face (the face of the left prism that connects to the right prism): \[ \text{Overlapping Area} = L_2 \times H_1 = 6 \times 8 = 48 \text{ mm}^2 \]
Step 4: Total Surface Area Calculation
Now, we can combine the surface areas and subtract the overlapping area: \[ \text{Total Surface Area} = \text{Surface Area}_1 + \text{Surface Area}_2 - \text{Overlapping Area} \]
Thus: \[ \text{Total Surface Area} = 376 + 216 - 48 = 544 \text{ mm}^2 \]
So, the total surface area of the figure is:
\[ \boxed{544} \text{ mm}^2 \]