How to Make 3D Polygons With Triangles

Geometry teachers and textbooks love to encourage students to draw pictures to help think through situations. Drawings are particularly useful when it comes to surface area and volume polygon problems. Yet, most students have difficulty making the three-dimensional, or 3D, figures they need, especially when triangles are involved. Learning how to successfully draw pyramids and triangular prisms provides a foundation for solving geometry problems that use them. Use a ruler or straight edge at first until you become skilled at drawing the lines needed.

Things You'll Need

  • Ruler or other straight edge
  • Writing utensil

Instructions

  1. Pyramids

    • 1

      Draw two parallel diagonal lines of the same length.

    • 2

      Connect the tops of the two lines and the bottoms of the two lines with a straight line for each set. Use the ruler or straight edge to get each line in place and then trace along the edge. This forms what looks like a parallelogram but actually represents a square base.

    • 3

      Draw a dot straight above the center of the base.

    • 4

      Line the edge of the ruler up so that it runs through both one of the corners of the base and the dot above. Trace along the edge, then repeat for each corner. This creates the four triangle faces of the pyramid.

    • 5

      Label any dimensions, such as side length or height, given in the problem.

    Triangular Prism

    • 6

      Draw a triangle. Pay attention to the directions and, if they call for a right triangle, make one of the corners an "L" shape.

    • 7

      Place the ruler against one of the corners of the triangle, then use it to draw a diagonal line out away from the triangle. Measure the line as you draw it.

    • 8

      Draw two more lines from the other two corners. Make them parallel with the first line and the same exact length. So, if the first line you drew was 3 inches, make the other 2 lines 3 inches as well.

    • 9

      Connect the ends of the three lines. This forms the triangular base at the other end of the prism. The lines that you make should be parallel to the sides of the original triangle.

    • 10

      Label any lengths of the faces, which are rectangles, or bases that the problem gives you.

Tips & Warnings

  • If the problem tells you the height of the 3D polygon, this refers to the distance between the two triangle bases for the prism, and the distance from the center of the base to the top point for the pyramid.
  • The "slant height" for a pyramid is the same as the height of one of its triangular faces.
  • You can make a tetrahedron by using the same method as the pyramid but drawing a triangle for the base.
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References

  • Photo Credit Ablestock.com/AbleStock.com/Getty Images

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