Name: 14m ConcietrionG.1A regular polygon is a shape that has equal sides and equal angles. There are only 3 regular polygons that can form tessellations by themselves. Other regular polygons can be used together to form a tessellation.Part 1Will the regular polygon tessellate?Part 2Describe the 3 regular polygons that will tessellate\begin{tabular}{|l|l|}\hline \multicolumn{1}{|c|}{ Regular Polygon } & Number of Sides \\\hline 1) & \\\hline 2) & \\\hline 3) & \\\hline\end{tabular}
Q. Name: 14m ConcietrionG.1A regular polygon is a shape that has equal sides and equal angles. There are only 3 regular polygons that can form tessellations by themselves. Other regular polygons can be used together to form a tessellation.Part 1Will the regular polygon tessellate?Part 2Describe the 3 regular polygons that will tessellate\begin{tabular}{|l|l|}\hline \multicolumn{1}{|c|}{ Regular Polygon } & Number of Sides \\\hline 1) & \\\hline 2) & \\\hline 3) & \\\hline\end{tabular}
Check Interior Angles: To determine if a regular polygon will tessellate, we need to check if the interior angles can fit together at a point without any gaps or overlaps. The formula for the interior angle of a regular polygon is (n−2)×180∘/n, where n is the number of sides.
Tessellation Criteria: Part 1: A regular polygon will tessellate if the interior angle divides evenly into 360°. This is because the angles at each vertex of the tessellation must add up to 360°.
Regular Polygons: Part 2: The three regular polygons that can tessellate by themselves are the equilateral triangle, the square, and the regular hexagon. We can check this by calculating their interior angles and seeing if they divide evenly into 360∘.
Equilateral Triangle: For the equilateral triangle (3 sides): The interior angle is (3−2)×180°/3=60°. Since 360°/60°=6, which is a whole number, equilateral triangles tessellate.
Square: For the square (4 sides): The interior angle is (4−2)×180∘/4=90∘. Since 360∘/90∘=4, which is a whole number, squares tessellate.
Regular Hexagon: For the regular hexagon (6 sides): The interior angle is (6−2)×180°/6=120°. Since 360°/120°=3, which is a whole number, regular hexagons tessellate.
List of Tessellating Polygons: Now, let's list the regular polygons that tessellate:1) Equilateral Triangle (3 sides)2) Square (4 sides)3) Regular Hexagon (6 sides)