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Basic Geometry

Basic Geometry

At a Glance - Perimeter & Circumference

The perimeter of a shape is the distance around the outside of the figure. It's pretty simple; just add up the lengths of each side.

Perimeter is often used to find the measurements needed to put borders around things: pictures, gardens, rooms, and buildings.

Let's see some examples:

1. What is the perimeter of a square with side lengths of 5 cm?Start by drawing a picture:
5 x 5 Square
If we add up the distance around the outside of the figure we get:
5 + 5 + 5 + 5 = 20
2. Find the perimeter of this object (all angles are 90°):
Wait, some sides are missing. No problem, we can fill those by adding together or subtracting the opposite sides.
Now find the sum of all sides:
6 + 4 + 2 + 3 + 4 + 7 = 26 cm
3. A rectangular backyard (30 ft by 25 ft) needs to be fenced. However, one side (the longer side) of the yard is next to the house. If fencing is about $25/foot, how much will the fence cost?Draw a picture!
25 x 30 house
Since 30 ft of the perimeter is bordered by the house, we only need: 25 + 30 + 25 = 80 ft of fencing.
Each foot of fencing costs $25. So the total cost is:
80 ft x $25 = $2000

Circumference: the Perimeter of a Circle

Circumference = diameter × π = 2 × r × π= 2πr = dπ

One neat thing about circles is that all circles are similar. The ratio of any circle's circumference/diameter is equal to one very extraordinary number, π (or "pi").

circumference/ diameter = (pi)

It doesn't matter the size of the circle, this ratio will always equal π. π equals roughly 3.14159, and is often rounded to 3.14.

Don't believe it? Take a piece of string and wrap it around the circular base of a can, then use a ruler to measure that distance. Carefully measure the distance across the center of this circle (the diameter), then divide the first measurement by the second. You probably won't get exactly π, but you will be close.

For each Example we'll give the answer two ways, in terms of π and using 3.14 to approximate pi.

Example 1

What is the circumference of a circle with diameter 12 cm?

Circle (4)

To find the circumference we need to multiply the diameter by π.

c= d (pi) = 12 (pi)

c = 12 x 3.14

c = 37.68 cm or 12 (pi)

Example 2

Find the circumference of a circle with a radius of 3 cm.

Circle (5)

Example 3

Find the radius of a circle with circumference of 31.4 cm.

Circle (6)

In this problem we need to work backwards to find the radius. We start by plugging in the information we know:

c = d (pi)

31.4 = d x (pi)

Exercise 1

Find the perimeter of a regular octagon with sides equal to 4 cm.

Exercise 2

What is the perimeter of this figure?

Figure to find perimeter of

Exercise 3

The perimeter of an equilateral triangle is 30 cm. What is the length of each side?

Exercise 4

Find the circumference of this circle.

Purple Circle

Exercise 5

A circular trampoline has a net surrounding it that is 25.12 ft long.

What is the diameter of the trampoline?