To find the total surface area of the figure, we need to find the surface area of each rectangular prism and then subtract the area of the connecting sides.
For the rectangular prism on the left:
- Surface area = 2lw + 2lh + 2wh
- Surface area = 2(10)(8) + 2(10)(6) + 2(8)(6)
- Surface area = 160 + 120 + 96
- Surface area = 376 square millimeters
For the rectangular prism on the right:
- Surface area = 2lw + 2lh + 2wh
- Surface area = 2(6)(6) + 2(6)(6) + 2(6)(6)
- Surface area = 72 + 72 + 72
- Surface area = 216 square millimeters
Now, we add the surface areas of the two rectangular prisms:
Total surface area = 376 + 216
Total surface area = 592 square millimeters
However, we must subtract the area of the connecting sides between the two rectangular prisms. The connecting sides are the top and front faces of the larger rectangular prism, which have an area of 6 * 6 = 36 square millimeters each.
Total surface area = 592 - 2(36)
Total surface area = 592 - 72
Total surface area = 520 square millimeters
Therefore, the total surface area of the figure is 520 square millimeters.