Gauss's Area Formula for Irregular Shapes

Authors

  • Jacob Gechlik Saratoga High School
  • Hayk Sedrakyan UPMC---Sorbonne University, Paris, France

Keywords:

Shoelace theorem, area formulas, irregular polygons, alternative algorithms

Abstract

To find the area of an irregular shape, we break the shape into common shapes. Then we find the area of each shape and add them, but this approach does not always work. In this paper we investigate Gauss’s area formula (for irregular shapes), also known as the shoelace formula or the shoelace algorithm. This theorem is outside the scope of school program. Nevertheless, we provide several applications that emphasize the importance and usefulness of this theorem. Most of the applications provided in this paper are created by the authors.

References

Sedrakyan, H., & Sedrakyan, N. (2021). AMC 8 preparation book. Independently published.

Sedrakyan, H., & Sedrakyan, N. (2021). AMC 10 preparation book. Independently published.

Sedrakyan, H., & Sedrakyan, N. (2021). AMC 12 preparation book. Independently published.

Sedrakyan, H., & Sedrakyan, N. (2023). AIME preparation book. Independently published.

Sedrakyan, H., & Sedrakyan, N. (2023). AMC and AIME geometry must-know techniques. Independently published.

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Published

2024-07-02

How to Cite

Gechlik, J., & Sedrakyan, H. (2024). Gauss’s Area Formula for Irregular Shapes. Ohio Journal of School Mathematics, 97(1), 12–29. Retrieved from https://ohiomathjournal.org/index.php/OJSM/article/view/9651

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