Answer:
The surface area is 644 cm^2.
Explanation:
The first thing I did was to find the SA of the top figure (excluding the bottom face, I'll get to that later). The dimensions of the figure has a square base with sides measuring 3 cm and a height of 8 cm. So then, I solved the the SA of the exposed faces and did the following:
Green Figure SA = (3 x 3) + 4(8 x 3)
= (9) + 4(24)
= (9) + (96)
= 105 cm^2
Now we get to the red figure. The reason why I excluded the bottom face of the green figure was because it was reducing the SA of the top face of the red figure. Knowing that the figure has a width of 10 cm and a length of 12 cm, I did the following:
Red Figure Top Face = 10(12) - 3(3)
= 120 - 9
= 111 cm^2
Then the next step is to solve for the SA of the entire red figure. Using what I've got for the top face, I did the following:
Red Figure SA = 111 + 2(7 x 10) + 2(7 x 12) + 10(12)
= 111 + 2(70) + 2(84) + (120)
= 111 + (140) + (168) + 120
= 539 cm^2
The last step is to just add the two SA's.
SA = 105 + 539
SA = 644 cm^2