Perimeter = Distance Around OUTSIDE!

Lesson Plan - Get It!

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Polygons and Non-Polygons

Before learning more about perimeter, it helps to know about polygons.

A polygon is a closed shape made only of straight sides.

Examples of polygons:

• triangle
• rectangle
• square
• pentagon
• hexagon

A non-polygon has at least one curved side or is not fully closed.

Examples of non-polygons:

• circle
• heart shape
• open shape

This lesson focuses only on polygons because their straight sides make perimeter easy to measure.

What Does Perimeter Mean?

Perimeter is a measurement of length. That means perimeter must always include units.

For example:

• 12 centimeters
• 20 inches
• 8 meters

Writing only “12” is not enough. You must include the unit.

One way to picture perimeter is to imagine walking along the edge of a shape until you return to your starting point. The total distance you travel is the perimeter.

Finding the Perimeter of a Triangle

Look at this triangle:

• side 1 = 3 cm
• side 2 = 4 cm
• side 3 = 5 cm

Add the side lengths:

3 + 4 + 5 = 12

The perimeter is 12 cm.

Finding the Perimeter of a Rectangle

Rectangles have two long sides and two short sides.

Example:

• length = 10 m
• width = 5 m

Add all four sides:

10 + 5 + 10 + 5 = 30

The perimeter is 30 m.

There is also a rectangle perimeter formula:

P = 2L + 2W

This formula means:

• P = perimeter
• L = length
• W = width

You may use the formula or simply add all the sides together. Both methods work.

Finding the Perimeter of Regular Polygons

A regular polygon has sides that are all the same length.

For example, a regular hexagon has:

• 6 sides
• each side is 4 cm

Instead of adding 4 six times, multiply:

6 × 4 = 24

The perimeter is 24 cm.

You can use this shortcut for any regular polygon:

number of sides × side length = perimeter

Finding Perimeter on a Grid

Sometimes shapes appear on square grids.

If each side of a square equals 1 centimeter, count the outside edges carefully. Only count each edge once.

A good strategy:

1. Start at one corner.
2. Trace around the outside.
3. Count each side until you return to the start.

This helps you avoid missing sides or counting sides twice.

Finding Missing Side Lengths

Sometimes a problem gives the perimeter but leaves out a side length.

For example, a rectangle has:

• perimeter = 20 cm
• one side = 4 cm

Use the rectangle formula:

P = 2L + 2W

Substitute the numbers:

20 = 2(4) + 2W

Multiply:

20 = 8 + 2W

Subtract 8:

12 = 2W

Divide by 2:

W = 6

The missing width is 6 cm.

You can also solve some missing-side problems by thinking carefully about matching sides in rectangles. Opposite sides of a rectangle are always equal in length.

Common Mistakes to Avoid

• Forgetting units
• Counting one side twice
• Forgetting a side
• Finding the inside space instead of the outside distance

Remember:

Perimeter measures the OUTSIDE of a shape.

Area measures the INSIDE of a shape.

Quick Check

Answer these questions out loud.

Nice work! Now that you know how perimeter works, you are ready to practice finding the perimeter of different shapes in real-life situations.