To find the total surface area of the composite figure, we'll calculate the surface area of each rectangular prism separately and then adjust for the shared side where the two prisms connect.
Step 1: Calculate the surface area of each rectangular prism.
For the left rectangular prism:
- Length (L) = 10 mm
- Height (H) = 8 mm
- Width (W): Since the combined length is 16 mm and the right prism has a length of 6 mm, the width of the left prism is equal to the width of the right prism, which is 6 mm.
Using the surface area formula for a rectangular prism: \[ \text{Surface Area} = 2(LW + LH + WH) \] Plugging in the values for the left prism: \[ \text{Surface Area} = 2(10 \cdot 6 + 10 \cdot 8 + 6 \cdot 8) \] \[ = 2(60 + 80 + 48) = 2(188) = 376 , \text{mm}^2 \]
For the right rectangular prism:
- Length (L) = 6 mm
- Width (W) = 6 mm
- Height (H) = 6 mm.
Using the same surface area formula: \[ \text{Surface Area} = 2(LW + LH + WH) \] Plugging in the values for the right prism: \[ \text{Surface Area} = 2(6 \cdot 6 + 6 \cdot 6 + 6 \cdot 6) \] \[ = 2(36 + 36 + 36) = 2(108) = 216 , \text{mm}^2 \]
Step 2: Adjust for the shared face area.
The left prism and the right prism share one face (the face where the left prism connects to the right prism).
- The shared face has dimensions: height = 6 mm (the common height) and width = 6 mm (the width of the right prism).
- Area of shared face: \[ \text{Area} = 6 \cdot 6 = 36 , \text{mm}^2 \]
Step 3: Calculate the total surface area.
The total surface area of the figure is the combined surface area of both prisms minus the shared area: \[ \text{Total Surface Area} = \text{Surface Area of Left Prism} + \text{Surface Area of Right Prism} - \text{Area of Shared Face} \] \[ = 376 + 216 - 36 = 556 , \text{mm}^2 \]
Final Answer: The total surface area of the composite figure is 556 mm².