Question

arthur is drawing the faces of a rectangular prism so that he can make the net and a model of the prism. he has drawn 4 of the faces so far, which are shown in the diagram below. diagram of 4 faces drag the 2 missing faces to the box so that he can make the net. missing faces section with 5 face options

Explanation:

Step1: Analyze the given faces

The drawn faces include two green - colored rectangles (let's assume their dimensions: from the grid, let's say the green ones have a height of, for example, \(h\) and a width of \(w_1\)) and two red - colored rectangles (with height \(h\) and width \(w_2\)). A rectangular prism has 6 faces: 3 pairs of congruent rectangles. So we already have two pairs (green - green and red - red), and we need the third pair.

Step2: Identify the missing face dimensions

The third pair of faces should have dimensions equal to \(w_1\times w_2\) (the product of the widths of the green and red rectangles). Looking at the "Missing Faces" options, we need to find two congruent rectangles with dimensions \(w_1\times w_2\). From the grid - like structure of the faces, we can see that the second (middle - small) face (the one with a smaller grid, let's check the number of squares: if green has, say, \(a\times b\) squares and red has \(c\times b\) squares, then the missing face should have \(a\times c\) squares) is the one that forms the third pair. So we need to drag the two congruent faces that match the \(w_1\times w_2\) dimensions, which is the second (the small - sized with the purple grid) face (and its congruent counterpart, but since we need two, and the second face is the one that fits the \(w_1\times w_2\) dimension, we drag the two faces that are congruent to the second face in the "Missing Faces" row.

Answer:

The two missing faces are the second (the middle - small) face in the "Missing Faces" row (and its congruent copy, but since we need to drag two, we select the two faces with dimensions equal to the product of the non - matching sides of the already drawn green and red faces, which is the second face in the "Missing Faces" section and its congruent one). In terms of the position, if the "Missing Faces" are in a row: the second face (the one with the smaller purple grid) and its congruent face (but since the options are given, we identify that the second face (the middle - small) is the correct one to form the third pair of faces of the rectangular prism net. So we drag the second face (the middle - small purple - gridded face) and its congruent face (the same as the second one) to the box.