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How to Make a Heptagon With 6 Equilateral Triangles

Updated July 20, 2017

A heptagon is any seven-sided closed shape. A regular heptagon has seven equal sides and angles and is impossible to construct using a ruler and compass. The closest attempt was made more than 2,000 years ago by the Greek scientist Archimedes, but his math was faulty and his method can't be reproduced. However, with six equilateral triangles, which have equal sides and equal angles, anyone can construct an irregular heptagon.

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  1. Place a triangle in the centre of a piece of blank paper.

  2. Position two upside-down triangles on either side of the first so that their edges are touching.

  3. Add an upright triangle to the left and right of this shape to create a trapezoid with a base three times the length of the original triangle.

  4. Turn the last triangle upside down and place it on the page so that its uppermost edge is pressed against the base of the original triangle.

  5. Hold the triangles firmly in place with the palm of your hand. Trace around the outside edges of the shape with a pencil. Remove the triangles.

  6. Count the sides of the shape. If there are seven, you have correctly made an irregular heptagon.

  7. Tip

    If you don't have pattern blocks, you can draw and cut out equilateral triangles from thick paper or cardboard. Use two-sided tape or removable glue to attach the triangles to the paper if you have difficulty tracing them.

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Things You'll Need

  • 6 equilateral triangle pattern blocks

About the Author

Robin Elisabeth Black is a freelance writer from Fredericton, New Brunswick. She has a Bachelor of Arts and a Bachelor of Education in history, English and math from St. Thomas University and has experience writing in many different genres.

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