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. Faces such as: 8,18,2, and 9 are used on the rectangular prism
The area of each missing face is __ meters squared m²
The length of each missing edge is __ meters m
To find the area of the missing faces and the missing dimension, we need to first identify which faces are missing.
From the net, we can see that the dimensions are as follows:
Face 8: 6m x 3m = 18m²
Face 18: 6m x 3m = 18m²
Face 2: 2m x 3m = 6m²
Face 9: 3m x 3m = 9m²
The surface area of the prism is given as 102m², and we have already identified 18m² + 18m² + 6m² + 9m² = 51m².
Therefore, the combined area of the four faces labelled is 51m². To find the area of the missing faces, we subtract this from the total surface area:
102m² - 51m² = 51m²
So, the area of the missing faces is 51m².
To find the dimensions of the missing faces, we need to consider that each rectangular prism has three pairs of congruent faces that are opposite to one another. Therefore, the missing faces are opposite the known faces. This means that the dimensions of the missing faces are the same as the known faces, just arranged in a different order.
For face 8, the length and width can be interchanged, so the dimensions of the missing face opposite to it are 3m x 6m.
For faces 18 and 2, their dimensions are already equal to each other, so the missing faces opposite to them have the same dimensions as the known faces.
Therefore, the length of each missing edge is 6m and the area of each missing face is 18m².