Question

The net of a rectangular prism is shown below. The surface area of each face is labeled. Which values represent the dimensions, in inches, of the rectangular prism?

a) 2, 3, 8
b) 3, 4, 8
c) 12, 24, 32
d) 3, 4, 12

Answer 1

To find the dimensions of a rectangular prism based on its net, we look at the areas of individual faces. By utilizing known dimensions or scale factors, we deduce the prism's length, width, and height.

Step-by-step explanation:

To determine the dimensions of a rectangular prism based on the surface area of its faces when the net is given, we first identify the individual areas of each face and then deduce the corresponding length dimensions that would give us those areas. If one face of the prism (often a square or rectangular side) has a known dimension, or we know how the dimensions of different faces are related (like being scaled up by a factor), we can use this to find other dimensions.

For example, if we have a square with a side length of 4 inches and we know a similar square has dimensions that are doubled, the side length of the larger square is 4 inches x 2 = 8 inches. This is useful for understanding how scaling factors work and for solving various problems where we need to find dimensions based on scale.