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.On the tactile printout of the following graphs, d is 6 meters squared, b is 18 meters squared, e is 2 meters, and f is 9 meters. The missing face is labeled A and the missing dimension is labeled with a question mark.
To find the missing face A, we need to consider that the surface area of a right rectangular prism is given by the formula:
Surface Area = 2lw + 2lh + 2wh
Given that the total surface area is 102 m², and we have the following areas filled in:
2lw = 18 m²
lh = 6 m²
wh = 9 m²
We can substitute these values into the formula:
18 + 6 + 9 + A = 102
33 + A = 102
A = 69
Therefore, the missing face A has an area of 69 m².
To find the missing dimension, we need to consider that the area of a face is given by the formula:
Area = length x width
Since face A is the missing face, and it is opposite to face B, which has an area of 18 m², the dimension of face A must be the same as face B. Therefore, the missing dimension is:
Length x Width = 18
Length x Width = 69 (since A = 69)
Since the dimensions of a rectangle are usually whole numbers, a possible set of dimensions for face A could be 3 m x 23 m.