To find the total surface area of the figure, we need to calculate the surface area of each rectangular prism and then add them together.
For the smaller rectangular prism:
- The surface area of the front and back faces (height x width) is 8 mm x w mm = 8w mm^2
- The surface area of the top and bottom faces (length x width) is 10 mm x w mm = 10w mm^2
- The surface area of the left and right faces (length x height) is 10 mm x 8 mm = 80 mm^2
Total surface area of smaller rectangular prism = 2(8w) + 2(10w) + 2(80) = 16w + 20w + 160 = 36w + 160 mm^2
For the larger rectangular prism:
- The surface area of the front and back faces (height x width) is 6 mm x 6 mm = 36 mm^2
- The surface area of the top and bottom faces (length x width) is 6 mm x 6 mm = 36 mm^2
- The surface area of the left and right faces (length x height) is 6 mm x 6 mm = 36 mm^2
Total surface area of larger rectangular prism = 2(36) + 2(36) + 2(36) = 72 + 72 + 72 = 216 mm^2
Therefore, the total surface area of the figure is the sum of the surface areas of the two rectangular prisms: 36w + 160 + 216 = 36w + 376 mm^2.