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.

Answer 1

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.