Perimeter and Circumference 

Hello. My name is Vickie Vickery and I have been a Middle and High School Math teacher for 14 years. Today's lesson will be useful to students taking Math in the 7th and 8th grade. On the following pages students will learn how to find the perimeter of polygons and the circumference of circles.

Perimeter of Polygons

Before we start our lesson, let/s review the definition of a polygon. A polygon is a simple closed shape made of line segments. Each line segment is called a side of the polygon, and the point where two sides of the polygon meet is called a vertex. Polygons are named according to the number of sides.

The word perimeter comes from the Greek prefix peri-, which means "around" and the Greek word metron, which means "measure." Thus, perimeter of a polygon means the measure around the polygon or the distance around it. Therefore, the perimeter is found by adding the lengths of the sides. It is measured as a certain number of units like inches, feet, meters, centimeters, and so forth. The most common plane shapes have formulas that make it easier to find the perimeter. Note that a formula uses symbols to express a mathematical fact.

Let's look at a rectangle. It has 4 sides, so by adding all four sides we say that P = l+l+w+w, where P is perimeter of rectangle, l is length, and w is width. As you can see opposite sides of the rectangle are congruent, so we can use the formula P = 2L +2W.

Now let's look at a square. We can write the formula for a square as P = s+s+s+s (s is the length of one side of a square). Since the four sides of the square are congruent, we can write the formula as P = 4s.

When a polygon has sides that are equal in length and angles that are equal in measure, it is called a regular polygon. Therefore all polygons that are regular you can multiply the number of sides by the length to get the perimeter.

The formula for a triangle is P = a + b + c, where a, b, and c stand for the length of each side of a triangle. If the triangle is an equilateral triangle, the formula would be P = 3s, where s is the length of one of the congruent sides.

As you may have noted so far to find the perimeter of any polygon, all you have to do is add up all the length of measure of each side of the polygon. Also this holds true for simple closed curves.


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