Area and Perimeter of Regular Polygons Review

Have the students get into small groups and distribute materials. Students should explore and discuss within their groups which polygons are regular. Teacher will act as a facilitator during group work. Then, as a class, teacher will lead students in a discussion on their findings and the following concepts and definitions will be addressed.
regular polygon- A polygon that is equiangular (all angles are equal) and equilateral (all sides are equal).

altitude of a triangle - The perpendicular distance between a vertex of a triangle and the side opposite that vertex. Sometimes called the height of a triangle.

Note: Since there are 3 vertices in every triangle, there are also 3 altitudes in every triangle! The altitude of the triangle depends on the vertex and the opposite side (or base) you are using.

base of a polygon - For two-dimensional figures, any side can be a base. Typically, however, the bottom side, on which the polygon 'sits,' is called the base.

Note: Any side of a triangle can serve as a base. So any triangle has three bases.

convex - If, when you join any two points inside a figure, the resulting line segment also lies inside the figure, then the figure is convex.

Note: A convex polygon is a polygon that has all of its interior angles less than 180 degrees.

concave - If, when you join any two points inside a figure, the resulting line segment goes outside the figure, then the figure is concave. Also called non convex.

Note: A concave polygon is a polygon with at least one interior angle greater than 180 degrees. One way to remember this is to think of concave polygons being like caves - there's a way to get "in" them. Hence a concave polygon could never be regular.

area of a polygon - A measurement of the region enclosed by the sides of a polygon. The area is always expressed in squared units.
perimeter of a polygon - The sum of the lengths of the sides of a polygon