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Draw the net of a triangular prism with an equilateral triangle cross-section, given a partial net showing one base and one rectangular face.

Mathematics

ScanSolve AI Answer

Step-by-step solution

3 steps

To complete the net of a triangular prism, we need two triangular bases and three rectangular faces. The problem states the cross-section is an equilateral triangle, meaning all sides of the triangle are equal, and thus all three rectangular faces will have the same width (equal to the side length of the triangle).

The given figure shows one equilateral triangle attached to one rectangular face. This represents one base and one lateral face of the prism.

  1. Identify the dimensions.

    From the given partial net, the base of the equilateral triangle is equal to the width of the rectangular face. Let this width be ww. The height of the rectangular face is the height of the prism, let it be hh.

  2. Add the remaining rectangular faces.

    A triangular prism has three rectangular faces. Since one is already shown, two more identical rectangular faces (each with dimensions w×hw \times h) need to be added. These should be placed adjacent to the existing rectangle, forming a strip of three rectangles.

  3. Add the second triangular base.

    The prism needs a second equilateral triangular base (with side length ww). This triangle should be attached to one of the rectangular faces, typically on the opposite side of the rectangular strip from the first triangle, or on the same side but offset.

    Here is the completed net:

          /\
         /  \
        /____\
        |    |____|____|
        |    |    |    |
        |    |    |    |
        |____|____|____|
               /\
              /  \
             /____\
    

    In this diagram:

    • The top triangle is the first equilateral base.
    • The three rectangles in the middle form the lateral surfaces of the prism. The leftmost rectangle is the one provided in the original image.
    • The bottom triangle is the second equilateral base.
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