Perimeter: Dimensions & Units

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Dimensions & Units

📖 Perimeter Study Guide

1. What Is a Dimension?

A dimension tells us how many independent directions we need to measure a shape. Refer to the Dimensions & Units guide on the Area Page for details on dimensions and the metric/US customary systems.
• A line or boundary is 1-dimensional (1D) — it has only length.
• A flat surface is 2-dimensional (2D) — it has width and height.
• A solid object is 3-dimensional (3D).

2. Units of Perimeter

Because perimeter measures the boundary of a shape (a 1D length), it is always measured in linear units (e.g.,

m

cm

ft

in

), never in square units (which are for area). For example, if a rectangle has sides of

5\text{ m}

and

3\text{ m}

, its perimeter is

16\text{ m}

(linear), while its area is

15\text{ m}^2

(square).

Rectangle (5m × 3m)

Triangle (3m - 4m - 5m)

Circle (r = 3m)

3. Converting Length Units

To convert perimeter, use the standard length conversion formulas from the Formula Sheet:
• Metric:

1\text{ m} = 100\text{ cm} = 1{,}000\text{ mm}

1\text{ cm} = 10\text{ mm}

1\text{ dm} = 10\text{ cm}

.
• US Customary:

1\text{ mi} = 1{,}760\text{ yd}

1\text{ yd} = 3\text{ ft}

1\text{ ft} = 12\text{ in}

.
• Multiply when converting from a larger unit to a smaller one (e.g.,

3\text{ ft} \times 12 = 36\text{ in}

). Divide when going from smaller to larger.

US Customary Length Conversions

1\text{ mi} = 1{,}760\text{ yd} \\ 1\text{ yd} = 3\text{ ft} \\ 1\text{ ft} = 12\text{ in}

Metric Length Conversions

1\text{ m} = 10\text{ dm} \\ 1\text{ dm} = 10\text{ cm} \\ 1\text{ cm} = 10\text{ mm}

4. Perimeter vs. Area Scaling

When you enlarge a shape by a percentage (scaling all its dimensions by a scale factor

k

):
• Perimeter (1D) scales linearly by

k

. The ratio of the new perimeter to the old is

k:1

.
• Area (2D) scales quadratically by

k^2

. The ratio of the new area to the old is

k^2:1

.

Example: If you increase all sides of a shape by

50\%

, the scale factor is

1.5 = 3/2

.
• The ratio of new perimeter to old perimeter is

\mathbf{3:2}

.
• The ratio of new area to old area is

(3/2)^2 = \mathbf{9:4}

5. Curiosity: The Rope Around the Earth

Imagine wrapping a rope tightly around the Earth's equator (assuming the Earth is a perfect sphere of radius

R

). Its length is the circumference

C_1 = 2\pi R

.
Now, suppose you want to add just enough rope so that the rope hovers exactly

1\text{ meter}

above the ground all the way around. The new radius is

R + 1\text{ m}

, and the new circumference is

C_2 = 2\pi(R + 1) = 2\pi R + 2\pi

.
The amount of rope you need to add is:

C_2 - C_1 = 2\pi(R + 1) - 2\pi R = 2\pi \approx 6.28\text{ meters}

Surprisingly, it does not depend on the radius of the Earth! Whether wrapping a tennis ball or the entire Earth, you only need to add about

6.28\text{ m}

of rope. This is because the relationship is linear (1-dimensional), a concept we will explore in future topics.

Mastering SealMath: Ratio & Unit Answers

• For ratio problems: enter your answer in a:b format (e.g., type 3:2 or 9:4). Make sure the ratio is fully simplified (no common factors).
• For calculation problems: enter your numerical answer as P = value. The unit is shown in the question, so do not type it.

Learning Topics

Frequently Asked Questions

What unit is used for perimeter?

Since perimeter is a one-dimensional length (boundary), it is measured in linear units like meters (m), centimeters (cm), feet (ft), or inches (in). It is never measured in square units, which are reserved for area.

What is perimeter?

Perimeter is the total boundary of a two-dimensional shape. It includes both the outer boundary and any inner boundaries (like the edges of holes inside the shape).