First, let's find the surface area of each individual rectangular prism.
Surface area of the larger rectangular prism:
- Front and back faces: 2(13.7cm x 4cm) = 54.8cm^2
- Top and bottom faces: 2(13.7cm x 3cm) = 82.2cm^2
- Side faces: 2(4cm x 3cm) = 24cm^2
Total surface area of the larger rectangular prism = 54.8cm^2 + 82.2cm^2 + 24cm^2 = 161cm^2
Surface area of the smaller rectangular prism:
- Front and back faces: 2(6.2cm x 3cm) = 37.2cm^2
- Top and bottom faces: 2(6.2cm x 7.5cm) = 93cm^2
- Side faces: 2(3cm x 7.5cm) = 45cm^2
Total surface area of the smaller rectangular prism = 37.2cm^2 + 93cm^2 + 45cm^2 = 175.2cm^2
Next, calculate the total surface area of the composite figure by adding the surface area of both rectangular prisms and subtracting the areas that are hidden:
Total surface area = (161cm^2 + 175.2cm^2) - (13.7cm x 3cm) = 336.2cm^2 - 41.1cm^2 = 295.1cm^2
So, the total surface area of the 3D composite figure when stacked on top of each other is 295.1 square centimeters.