The perimeter of the lawn, or the distance of the fencing required to enclose the lawn is equal to:

30 m + 30 m + 12 m + 12 m = 84 m

Therefore, the perimeter of a shape is found by adding up all of the side lengths of a shape. But for a rectangle, we can simplify the previous calculation a bit:

A rectangle has 4 sides, with 2 pairs of equal sides, so it is appropriate to group the equal side lengths together in one term.

A square has 4 sides, all of equal length, so we can do a similar simplification of the formula with a square resulting in the following:

For most shapes, even irregular shapes, it is best to use the approach of summing the different side lengths to find perimeter. But for circles, we have to do something a little bit different (as you'll see below).

To calculate the area of this shape, we use the following formula:

You’ll notice that when we calculate area, our units are squared. In the example above, we are multiplying 12 by 30, but we are also multiplying meters (m) by meters to get meters squared (m²). When we talking about volume, we will see that our units are cubed (ex. m³) and we will discuss this in greater detail.

It would be incorrect to say that the area of the rectangle is 360 m; area is measured in square units so we must say that the are of the lawn is 360 m².

Area: Worked Examples

The following table gives an outline of the new variables we see in circle geometry (π, r, and d):

In the following video, I go over some practice with circumference and area of circles.

Perimeter and Area Summary

I've summarized the key formulas we used for perimeter and area calculations below. As I've stated multiple times in my videos, I highly recommend having some understanding of the development of these formulas because they will be much easier to remember, use, and employ in more challenging situations.

Perimeter and Area: Putting it All Together (including Composite Shapes)

*Will be third video added above shortly.

(Optional Extensions) Area: The Area Model for Multiplication

Area models for multiplication and division can help students better conceptualize multiplication and division. By using the area model, students can see why common algorithms for multiplication and division work, rather than just memorizing them on their own. The area model can also be helpful for teaching students how to factor and expand binomials. If you’re interested in learning more, check out the video and the article below.

Area Model - Article

Area Model for Multiplication - Video

(Optional Extensions) Area & Perimeter: Where do the formulas come from?

If you’re curious about where some of these formulas come from check out the following videos:

Visual Proof of the Area of a Triangle

Proof of Area of a Circle