Find the surface area of the rectangular prism
6km bottom middle
3km bottom right
7km upper right
To find the surface area of a rectangular prism, we must calculate the area of each of the six faces and then add them all together.
1. The bottom face:
Since the bottom of the rectangular prism is divided into two rectangles, we will calculate the area of each rectangle separately.
Area of the first rectangle = 6 km * 3 km = 18 km^2
Area of the second rectangle = 3 km * 7 km = 21 km^2
Total area of the bottom face = 18 km^2 + 21 km^2 = 39 km^2
2. The top face:
Since the top face is also divided into two rectangles, we will calculate the area of each rectangle separately.
Area of the first rectangle = 6 km * 3 km = 18 km^2
Area of the second rectangle = 3 km * 7 km = 21 km^2
Total area of the top face = 18 km^2 + 21 km^2 = 39 km^2
3. The front face:
Area of the front face = 6 km * 7 km = 42 km^2
4. The back face:
Area of the back face = 6 km * 7 km = 42 km^2
5. The left face:
Area of the left face = 3 km * 7 km = 21 km^2
6. The right face:
Area of the right face = 3 km * 7 km = 21 km^2
Now, we add up the areas of all six faces to find the total surface area:
39 km^2 + 39 km^2 + 42 km^2 + 42 km^2 + 21 km^2 + 21 km^2 = 204 km^2
Therefore, the surface area of the rectangular prism is 204 km^2.