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