2- and 3-Dimensional Figures

Polygons A polygon is a closed figure formed by a finite number of coplanar segments called sides such that they sides that have a common endpoint are noncollinear and each side intersects exactly two other sides, but only at their endpoints (vertex)

Concave If any lines contain any point in the interior of the polygon, then it is concave

Convex If none of the lines contain any point in the interior of the polygon, then it is convex

Regular Polygons A convex polygon that is both equilateral and equiangular is called a regular polygon

Perimeter, Circumference, and Area Perimeter – the distance around a figure Circumference – the distance around a circle Area – the amount of space inside a figure

Polyhedrons A solid with all flat surfaces that enclose a single region of space Each flat surface (face) is a polygon The segments where the faces intersect are called edges The point where three or more edges intersect is called a vertex

Prism A polyhedron with two parallel congruent faces (bases) connected by parallelogram faces

Pyramid A polyhedron that has a polygonal base and three or more triangular faces that meet at a common vertex

Cylinder A solid with congruent parallel circular bases connected by a curved surface

Cone A solid with a circular base connected by a curved surface to a single vertex

Sphere A set of points in space that are the same distance from a given point. It has no faces, edges, or vertices

Regular Polyhedrons A polyhedron where all of the faces are regular congruent polygons and all of the edges are congruent. There are exactly five types of regular polyhedrons.

Surface Area and Volume Surface Area – a two-dimensional measurement of the surface of a solid figure; it is the sum of the areas of each face Volume – the measure of the amount of space enclosed by a solid figure

Questions What are some common applications of perimeter, area, surface area, and volume? Are there any careers that employ these measures? How do you use these measures?