Answer:
See below.
Step-by-step explanation:
The top is a square 3 cm by 3 cm.
The other 4 sides are rectangles. Each one is 4 cm by 3 cm.
Front: 4 cm * 3 cm = 12 cm^2
Back: 4 cm * 3 cm = 12 cm^2
Right: 4 cm * 3 cm = 12 cm^2
Left: 4 cm * 3 cm = 12 cm^2
Top: 3 cm * 3 cm = 9 cm^2
TOTAL: 12 cm^2 + 12 cm^2 + 12 cm^2 + 12 cm^2 + 9 cm^2
TOTAL: 57 cm^2
Bottom prism (blue):
Front: 5 cm * 6 cm = 30 cm^2
Back: 5 cm * 6 cm = 30 cm^2
Right: 5 cm * 6 cm = 30 cm^2
Left: 5 cm * 6 cm = 30 cm^2
Bottom: 5 cm * 5 cm = 25 cm^2
Top: 5 cm * 5 cm - 3 cm * 3 cm = 25 cm^2 - 9 cm^2 = 16 cm^2
TOTAL: 30 cm^2 + 30 cm^2 + 30 cm^2 + 30 cm^2 + 25 cm^2 + 16 cm^2
TOTAL: 161 cm^2
Explanation for area of top of bottom (blue) prism.
Notice that the entire bottom of the top (yellow) prism is connected to the bottom prism, so there is no area of the bottom of the top prism that adds to the total surface area of the composite solid. With the bottom prism's top surface it is different. Since the top surface of the blue prism is larger than the bottom surface of the yellow prism, there is a bit of top surface of the blue prism that is seen. That area is the area of the top surface of the blue prism minus the area of the bottom surface of the top prism.
5 cm * 5 cm = 3 cm * 3 cm = 25 cm^2 - 9 cm^2 = 16 cm^2
The area of the top surface of the blue prism is 16 cm^2
Total surface area of the composite solid:
57 cm^2 + 161 cm^2 = 218 cm^2
