What is Perimeter? — Mathematics

Definition 28.3 Primary & Middle School Mathematics · Chapter 28 — Measures and Perimeter

The perimeter of a polygon is the total length of its border: add the lengths of all its sides (in the same unit!). Shortcuts for the classics:

\text{rectangle: } P = 2 \times (L + w), \qquad \text{square: } P = 4 \times c .

Examples

Example 28.4

A rectangular garden $12$ m by $7$ m:

P = 2 \times (12 + 7) = 2 \times 19 = 38 \text{ m}

of fence. A square photo frame of side $18$ cm: $P = 4 \times 18 = 72$ cm.

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Definition 43.1 Primary & Middle School Mathematics · Chapter 43 — Perimeter, Area, Volume

The perimeter of a figure is the total length of its border. It is measured in units of length: millimeters (mm), centimeters (cm), meters (m), kilometers (km), with

1 \text{ km} = 1000 \text{ m}, \qquad 1 \text{ m} = 100 \text{ cm}, \qquad 1 \text{ cm} = 10 \text{ mm}.

Examples

Example 43.2

A rectangle of length $L$ and width $w$ has perimeter

P = L + w + L + w = 2 \times (L + w).

For a $7$ cm by $4$ cm rectangle: $P = 2 \times (7 + 4) = 2 \times 11 = 22$ cm. A square of side $c$ has perimeter $4c$ .

Example 43.7 (Composite figures)

An L-shaped room is a $6$ m $\times$ $4$ m rectangle with a $2$ m $\times$ $2$ m square corner removed. Its area, step by step:

full rectangle: $6 \times 4 = 24$ m $^2$ ;
removed square: $2 \times 2 = 4$ m $^2$ ;
remaining area: $24 - 4 = 20$ m $^2$ .

Its perimeter is not $20$ anything: walking around the L, the border still measures $6 + 4 + 6 + 4 = 20$ m — the two cuts of the corner replace two equal pieces of wall. Same number by coincidence, but square meters for one, meters for the other!

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Examples

Examples

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