Geometry

GED Mathematical Reasoning: Perimeter and Cirumference

Perimeter

The perimeter is the distance around a two-dimensional shape. The perimeter of any polygon is the sum of the lengths of all the sides.

meas54

Circle

Another basic shape we need to talk about is the circle. A circle doesn’t have straight sides like a rectangle or triangle so you may be wondering: How do we calculate a circle’s perimeter? Well, first of all, when it’s a circle we’re dealing with we don’t call it perimeter. The distance around a circle is called CIRCUMFERENCE.

Before we talk about how to find the circumference of a circle, we need to discuss radius and diameter.

The DIAMETER of a circle is the distance across. The RADIUS of a circle is the distance from the center of the circle to the outer edge. You can think of the radius as being half the diameter OR you can think of the diameter as being twice the radius.

There is one more thing you need to know in order to calculate circumference. To calculate the circumference of a circle, we need to use a value called “PI”. Pi is the ratio of the circumference to the diameter of any circle and always equals the same value: approximately 3.14. It’s such an important value in mathematics that we have a special symbol $\pi$ to represent pi.

$pi = \pi \approx 3.14$

Now let’s put this all together.

To find the circumference of a circle, multiply the diameter times pi:

$C = \pi \times d$

There’s another way to state this, since the diameter equals twice the radius. It is:

$C = \pi \times 2 \times r$

Both versions of the circumference formula are important to know because in some situations you will be given a radius and in others you will be given the diameter.

Example 1

Joe would like to put a fence around his rectangular garden. The garden’s length measures 15.3 feet and its width measures 8.2 feet. Find the total amount of fencing Joe will need to purchase.

Before we do any math, let’s identify the important information given in the problem. First note that Joe’s garden is a rectangle. A rectangle is a shape that contains four sides and four right angles, where opposite sides have the same length.

We’re also told that the length of the garden is 15.3 feet and the width is 8.2 feet. Even though we are only given two side measures, we actually know the length of all four sides of the garden since – in a rectangle – opposite sides have the same length. Let’s draw a picture to represent the garden with all four side measures labeled:

$math 198$

Finally, we are being asked to determine the amount of fencing needed. Since fencing goes around an area, we need to calculate the distance around the rectangle. Formally, the distance around a rectangle is called the perimeter, denoted by a capital letter “P”.

To calculate the perimeter of a rectangle, add the lengths of all four sides. So to find the perimeter of Joe’s garden, we’ll add:

$P = 15.3ft + 15.3ft + 8.2ft + 8.2ft = 47ft$

Example 2

Find the circumference of a circle having a radius equal to 20 inches.

It may be helpful to make a sketch of the circle on your paper with the given information labeled.

$math 199$

In this example, we are given the radius so to find the circumference we must use the second formula and multiply $\pi$ times two times the radius. And remember, we need to use 3.14 as the value for $\pi$ .

So we have:

$C = 3.14 \times 2 \times 20$

$C = 125.6$

So the circumference of, or distance around, a circle with a radius of 20 inches is 125.6 inches.

$math 200$