Question

1. what is a net for the figure below? label the net with its dimensions. 2 in. 5 in. 1 in.

Explanation:

Step1: Recall the net of a rectangular prism

A rectangular prism has 6 faces. The net consists of 6 rectangles. There are 3 pairs of identical rectangles.

Step2: Identify the dimensions of each face

• There are two rectangles with dimensions \(5\times2\) (length \(5\) in and height \(2\) in).
• There are two rectangles with dimensions \(5\times1\) (length \(5\) in and width \(1\) in).
• There are two rectangles with dimensions \(2\times1\) (height \(2\) in and width \(1\) in).

Answer:

The net of the rectangular prism (a type of cuboid) will have six rectangles. Two rectangles of size \(5\times2\) inches, two rectangles of size \(5\times1\) inches and two rectangles of size \(2\times1\) inches. One possible arrangement of the net is:

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(Note: The actual drawing of the net would be a 2 - D layout of these rectangles connected appropriately. For example, a common net layout for a rectangular prism is a central rectangle (say \(5\times1\)) with rectangles attached to its four sides: two \(5\times2\) rectangles attached to the longer sides of the central \(5\times1\) rectangle and two \(2\times1\) rectangles attached to the shorter sides of the central \(5\times1\) rectangle. Then another \(5\times1\) rectangle attached to one of the \(2\times1\) rectangles)