Polygons and Triangles Study Guide

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Updated on Oct 5, 2011

Introduction to Polygons and Triangles

Geometry existed before the creation.

—PLATO, classical Greek philosopher (427 B.C.E.–347 B.C.E.)

After introducing polygons, this geometry lesson reviews the concepts of area and perimeter and finishes with a detailed exploration of triangles.

We're surrounded by polygons of one sort or another, and sometimes, we even have to do math with them. Furthermore, geometry problems on tests often focus on finding the perimeter or area of polygons, especially triangles. So this lesson introduces polygons and shows you how to work with triangles. The next lesson deals with rectangles, squares, and circles.


What Is a Polygon?

A polygon is a closed, planar (flat) figure formed by three or more connected line segments that don't cross each other. Familiarize yourself with the following polygons; they are the three most common polygons appearing on tests —and in life.

Polygons and Triangles

Perimeter of Polygons

Perimeter is the distance around a polygon. The word perimeter is derived from peri, which means around (as in periscope and peripheral vision), and meter, which means measure. Thus, perimeter is the measure around something. There are many everyday applications of perimeter. For instance, a carpenter measures the perimeter of a room to determine how many feet of ceiling molding she needs. A farmer measures the perimeter of a field to determine how many feet of fencing he needs to surround it.

Perimeter is measured in length units, like feet, yards, inches, meters, and so on. To find the permineter of a polygon, add the lengths of the sides.

Example: Find the perimeter of the polygon below:

Polygons and Triangles

Solution: Write down the length of each side and add:

The notion of perimeter also applies to a circle; however, the perimeter of a circle is referred to as its circumference.

Area of Polygons

Area is the amount of space taken by a figure's surface. Area is measured in square units. For instance, a square that is 1 unit on all sides covers 1 square unit. If the unit of measurement for each side is feet, for example, then the area is measured in square feet; other possibilities are units like square inches, square miles, square meters, and so on.

Polygons and Triangles

You could measure the area of any figure by counting the number of square units the figure occupies. These first two figures below are easy to measure because the square units fit into them evenly, while the next two figures are more difficult to measure because the square units don't fit into them evenly.

Polygons and Triangles

Polygons and Triangles

Because it's not always practical to measure a particular figure's area by counting the number of square units it occupies, an area formula is used. As each figure is discussed, you'll learn its area formula. Although there are perimeter formulas as well, you don't really need them (except for circles) if you understand the perimeter concept: It is merely the sum of the lengths of the sides.


What Is a Triangle?

A triangle is a polygon with three sides, like those shown here:

Polygons and Triangles

The symbol used to indicate a triangle is . Each vertex—the point at which two lines meet—is named by a capital letter. The triangle is named by the three letters at the vertices, usually in alphabetical order: ABC.

Polygons and Triangles

There are two ways to refer to a side of a triangle:

  • By the letters at each end of the side: AB
  • By the letter—typically a lowercase letter—next to the side:

Notice that the name of the side is the same as the name of the angle opposite it, except the angle's name is a capital letter.

There are two ways to refer to an angle of a triangle:

  • By the letter at the vertex:A
  • By the triangle's three letters, with that angle's vertex letter in the middle:BAC or CAB


The sum of any two sides of a triangle must always be greater than the third side. Therefore, the following could not be the lengths of the sides of a triangle: 4-7-12.

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