The figure below is a net for a right rectangular prism. Its surface area is 102 m² and the area of some of the faces are filled in below. Find the area of the missing faces, and the missing dimension.

Question

The area of each missing face is __ meters squared m²
The length of each missing edge is __ meters m

Answer 1

To find the missing faces, we need to first identify the dimensions of the rectangular prism.

Looking at the net, we can see that the following faces are filled in:

- Front face = 20 m² (length * width)
- Top face = 18 m² (length * width)
- Right face = 24 m² (length * height)

Since the surface area of the prism is 102 m², we can set up an equation to find the total surface area:

102 = 2lw + 2lh + 2wh

Now, plug in the values of the filled in faces:

102 = 2(20) + 2(24) + 2(18)
102 = 40 + 48 + 36
102 = 84 + 36
102 = 120

Now, we can subtract the filled in face areas to find the missing faces:

Missing back face area = 120 - 20 - 24 - 18 = 58 m²

Now, we need to find the dimensions of the rectangular prism. We can see that the height is the missing edge, so let's solve for the height using the right face:

24 = length * height
24 = 8 * height
height = 3m

Therefore, the area of each missing face is 58 m² and the length of each missing edge is 3 meters.