Triangles Everywhere: Sum of Angles in Polygons
Students learn about regular polygons and the common characteristics of regular polygons. They relate their mathematical knowledge of these shapes to the presence of these shapes in the human-made structures around us, especially trusses. Through a guided worksheet and teamwork, students explore the idea of dividing regular polygons into triangles, calculating the sums of angles in polygons using triangles, and identifying angles in shapes using protractors. They derive equations 1) for the sum of interior angles in a regular polygon, and 2) to find the measure of each angle in a regular n-gon. This activity extends students’ knowledge to engineering design and truss construction. This activity is the middle step in a series on polygons and trusses, and prepares students for the Polygon and Popsicle Trusses associated activity.
Typical truss bridge components.Copyright Historic American Engineering Record, National Park Service, U.S. Department of the Interior http://npshistory.com/publications/oregon/historic_highway_bridges/glossary.htm
Civil engineers design buildings, bridges and towers using basic shapes such as triangles and squares. To make sure the structures are stable and safe, they design them to be able to withstand the anticipated loads without any deformation or bending. They make precise and accurate specifications and measurements, and then double-check their plans by making estimates to verify that the calculations are reasonable. Through this activity, students come to see trusses from an engineering point of view—as unique compositions of polygon shapes that are further broken down into triangle shapes, which serve as the strongest and least deformable shapes.
After this activity, students should be able to:
- Explain the components and common characteristics of regular polygons.
- Explain how to find the sum of the interior angles in a polygon of n sides.
- Develop an equation that shows the relationship between the number of sides of a polygon and the sum of its interior angles.
- Explain how the geometry of shapes impacts engineering bridge and truss design and stability.