To find the surface area of the composite figure, we need to break it down into simpler shapes and add up their surface areas. From the given dimensions, we can see that the composite figure consists of two rectangular prisms and a triangular prism.
The dimensions of the rectangular prism are 10 cm (length), 8 cm (width), and 24 cm (height). Therefore, its surface area is:
SA1 = 2lw + 2lh + 2wh
SA1 = 2(10 cm)(8 cm) + 2(10 cm)(24 cm) + 2(8 cm)(24 cm)
SA1 = 160 cm^2 + 480 cm^2 + 384 cm^2
SA1 = 1024 cm^2
The dimensions of the triangular prism are 5 cm (base), 12 cm (height), and 8 cm (length). Therefore, its surface area is:
SA2 = lb + 2[(1/2)bh + lh]
SA2 = (8 cm)(5 cm) + 2[(1/2)(5 cm)(12 cm) + (8 cm)(12 cm)]
SA2 = 40 cm^2 + 240 cm^2 + 96 cm^2
SA2 = 376 cm^2
The dimensions of the rectangular prism on top are 4 cm (length), 5 cm (width), and 12 cm (height). Therefore, its surface area is:
SA3 = 2lw + 2lh + 2wh
SA3 = 2(4 cm)(5 cm) + 2(4 cm)(12 cm) + 2(5 cm)(12 cm)
SA3 = 40 cm^2 + 96 cm^2 + 120 cm^2
SA3 = 256 cm^2
To find the total surface area of the composite figure, we add the surface areas of the three shapes:
Total surface area = SA1 + SA2 + SA3
Total surface area = 1024 cm^2 + 376 cm^2 + 256 cm^2
Total surface area = 1656 cm^2
Therefore, the surface area of the composite figure is 1656 cm^2.