Perimeter and Area

Background

When we deal with a closed shape we can draw on a piece of paper (known as a two-dimensional figure), we can talk about amount of distance the edge of that shape occupies, and the amount of area the shape encompasses...

Question

What is a perimeter? What is an area?

Answer

The perimeter is the length of the boundary of the shape. The area is the space enclosed by the shape.

Analysis

Let's start with a line segment that is 4 units long:



If we take this length and bend it at point 3 into a 90 angle in the up direction, we get this:



We can do this twice more (keeping the right angles made in the prior moves), we get this:



Let's talk about the distance around the figure - which is known as the perimeter.

As we saw when we started with the initial line, it's 4 units long. We can verify that with this current figure by adding up the individual distances. From (0,0) to (0,1) is 1 unit, (0,1) to (1,1) is 1 unit, (1,1) to (1,0) is 1 unit, and then back again from (1,0) to (0,0) is 1 unit. 1 + 1 + 1 + 1 = 4.

Now we can talk about the space within the 4 line segments. That space within the figure is called the area.

To calculate the area, we can count the number of squares with sides equal to 1. Just to be clear, we've made a square in the graph above (a plane figure with four equal sides and four right angles). There is one 1-unit square in the graph, and so we say the area is 1 square unit, or 1 unit square (can be said either way).

Let's look at another figure:



The perimeter, the distance around the edge of the figure, is 8 units (2 + 2 + 2 + 2).

The area is 4 units square. We can count the squares - we can see them in the figure. Another way we can find the area is to multiply one side of the figure by another side at a right angle to it. In this case, we have 2 units left to right and 2 units up and down, so that's 2 x 2 = 4 square units.

Let's talk about why this works.

If you take an ice cube tray, you can see that there are a certain number of spaces for ice going across and another number going up and down (mine are six long and two up and down). We can multiply the 2 and the 6 together (2 x 6 = 6 x 2) and get 12 spaces for ice. And so we can do the same for measuring the squares inside a square (and, in fact, some other shapes - we'll talk about those in further entries).

Vocabulary used:

For more information check out these links (comment to add your favourite link):

Where might you have come from?

Fact-orials Index

Geometry:

• Points, Line Segment, Line
• Intersecting, Parallel, Perpendicular Lines
• Defining a Circle and Right Angles

Where might we go?

Geometry:

• Squares