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.
To find the missing faces and dimensions, we first need to analyze the given information.
From the net, we can see that the dimensions of the right rectangular prism are as follows:
- Top face: 4m x 5m = 20m^2
- Front face: 4m x h = 4h m^2
- Side face: 5m x h = 5h m^2
Given that the total surface area of the prism is 102m^2, we can set up the equation:
2(20) + 4h + 5h = 102
40 + 9h = 102
9h = 62
h = 6.89 (approx)
Therefore, the missing dimension is approximately 6.89m.
Now, we can calculate the missing areas:
- Back face = 4m x 6.89m = 27.56m^2
- Bottom face = 5m x 6.89m = 34.45m^2
Therefore, the missing faces are the back face and bottom face with areas of 27.56m^2 and 34.45m^2, respectively.