This activity walks students through constructing an octagon and, separately, a dodecagon, both using Cartesian coordinate geometry. Two graphing grids are included in the worksheet for the construction of the polygons.
Once a polygon is constructed, students will:
Measure the angles of the polygon
Measure one central angle of the polygon
Determine the sum of the central angles
Measure the side lengths of the polygon
Use the side lengths to calculate the perimeter
Divide the polygon into equally sized triangles
Measure all three angles of one of the triangles
Construct the height of that triangle (which becomes the apothem of the polygon)
Calculate the apothem or height of the triangle using the Pythagorean Theorem
Calculate the area of the triangle and use this to determine the area of the polygon
Calculate the area of the polygon using the perimeter and apothem.
One polygon construction worksheet could be used as an in-class activity and the other as a homework or quiz if the teacher desires.
Constructing and Analyzing Polygons Using Coordinate Geometry
by Anthony J. Pultrone
is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License