Basic Math and Pre-Algebra For Dummies (77 page)

Every other polygon is an
irregular polygon
(see Figure 
16-5
).

A circle is the set of all points that are a constant distance from the circle's center. The distance from any point on the circle to its center is called the
radius
of the circle. The distance from any point on the circle straight through the center to the other side of the circle is called the
diameter
of the circle.

Unlike polygons, a circle has no straight edges. The ancient Greeks — who invented much of geometry as we know it today — thought that the circle was the most perfect geometric shape.

Solid geometry is the study of shapes in
space
— that is, the study of shapes in three dimensions. A
solid
is the spatial (three-dimensional, or 3-D) equivalent of a shape. Every solid has an
inside
and an
outside
separated by the surface of the solid. Here, I introduce you to a variety of solids.

A
polyhedron
is the three-dimensional equivalent of a polygon. As you may recall from earlier in the chapter, a polygon is a shape that has only straight sides. Similarly, a polyhedron is a solid that has only straight edges and flat faces (that is, faces that are polygons).

The most common polyhedron is the
cube
(see Figure 
16-6
). As you can see, a cube has 6 flat faces that are polygons — in this case, all the faces are square — and 12 straight edges. Additionally, a cube has eight
vertexes,
or
vertices
(corners). Later in this chapter, I show you how to measure the surface area and volume of a cube.

Figure 
16-7
shows a few common polyhedrons (or polyhedra).

Later in this chapter, I show you how measure each of these polyhedrons to determine its volume — that is, the amount of space contained inside its surface.

One special set of polyhedrons is called the
five regular solids
(see Figure 
16-8
). Each regular solid has identical faces that are regular polygons. Notice that a cube is a type of regular solid. Similarly, the tetrahedron is a pyramid with four faces that are equilateral triangles.

Many solids aren't polyhedrons because they contain at least one curved surface. Here are a few of the most common of these types of solids (also see Figure 
16-9
):

• Sphere:
  A
  sphere
  is the solid, or three-dimensional, equivalent of a circle. A ball is a perfect visual aid for a sphere.
  
• Cylinder:
  A
  cylinder
  has a circular base and extends vertically from the plane. A good visual aid for a cylinder is a can of soup.
  
• Cone:
  A
  cone
  is a solid with a round base that extends vertically to a single point. A good visual aid for a cone is an ice-cream cone.
  

In the next section, I show you how to measure a sphere and a cylinder to determine their volume — that is, the amount of space contained within.

In this section, I introduce you to some important formulas for measuring shapes on the plane and solids in space. These formulas use letters to stand for numbers that you can plug in to make specific measurements. Using letters in place of numbers is a feature you'll see more of in Part V, when I discuss algebra.

Two important skills in geometry — and real life — are finding the perimeter and calculating the area of shapes. A shape's
perimeter
is a measurement of the length of its sides. You use perimeter for measuring the distance around the edges of a room, building, or circular pathway. A shape's
area
is a measurement of how big it is inside. You use area when measuring the size of a wall, a table, or a tire.

For example, in Figure 
16-10
, I give you the lengths of the sides of each shape.

 When every side of a shape is straight, you can measure its perimeter by adding up the lengths of all its sides.

Similarly, in Figure 
16-11
, I give you the area of each shape.