The figure below is a net for a right rectangular prism. Its surface area is 160 ft² and the area of some of the faces are filled in below. Find the area of the missing faces, and the missing dimension.
To find the missing faces and dimensions, we need to first understand the surface area of a right rectangular prism.
The surface area of a right rectangular prism is given by the formula:
SA = 2lw + 2lh + 2wh
Given that the surface area of the prism is 160 ft², we can use the given areas of some of the faces to find the missing faces and dimensions.
From the given net, we can see that:
- The area of face 1 is 48 ft² (length x width)
- The area of face 2 is 32 ft² (height x width)
- The area of face 5 is 40 ft² (length x height)
Using these areas, we can set up the following equations:
48 = l x w
32 = h x w
40 = l x h
Solving these equations, we find that:
- l = 6 ft
- w = 8 ft
- h = 5 ft
Now we can find the missing faces:
- The area of face 3 = l x h = 6 ft x 5 ft = 30 ft²
- The area of face 4 = l x h = 6 ft x 5 ft = 30 ft²
Therefore, the missing faces have areas of 30 ft² each and the missing dimension for these faces is the height, which is 5 ft.