Perimeter

The perimeter is the total distance around the outside of a shape. If you walked along every edge of a flat figure and measured how far you traveled, that distance is the perimeter. For circles, the perimeter has a special name: circumference.

Perimeter is a linear measurement — it’s measured in feet, inches, meters, or other units of length (not square units, which are for area).

Perimeter of a Rectangle

A rectangle has two lengths ($l$) and two widths ($w$). Add all four sides:

$P = l + w + l + w = 2l + 2w$

Example 1: A room is 14 ft long and 10 ft wide. Find the perimeter.

$P = 2(14) + 2(10)$

$P = 28 + 20$

$P = 48 \text{ ft}$

Answer: The perimeter is 48 feet.

Perimeter of a Square

A square has four equal sides of length $s$:

$P = 4s$

Example 2: A square tile is 8 inches on each side. Find its perimeter.

$P = 4(8) = 32 \text{ in}$

Answer: The perimeter is 32 inches.

Perimeter of a Triangle

A triangle has three sides. Add them all:

$P = a + b + c$

where $a$, $b$, and $c$ are the lengths of the three sides.

Example 3: A triangular garden bed has sides of 6 ft, 8 ft, and 10 ft. Find the perimeter.

$P = 6 + 8 + 10 = 24 \text{ ft}$

Answer: The perimeter is 24 feet.

Perimeter of Regular Polygons

A regular polygon has all sides equal. If it has $n$ sides, each of length $s$:

$P = n \times s$

Perimeter of Irregular Shapes

For any polygon — regular or not — the perimeter is simply the sum of all side lengths. Measure every side and add them up. There is no shortcut formula for irregular shapes.

Circumference of a Circle

A circle’s perimeter is called its circumference. It depends on the radius ($r$) or diameter ($d$), where $d = 2r$.

$C = 2\pi r = \pi d$

The value of $\pi$ (pi) is approximately $3.14159$. For most practical work, use $\pi \approx 3.14$ or the $\pi$ button on your calculator.

Example 4: A circular flower bed has a diameter of 12 ft. Find the circumference.

$C = \pi d = \pi(12) \approx 3.14 \times 12 = 37.68 \text{ ft}$

Answer: The circumference is approximately 37.68 feet.

Example 5: A wheel has a radius of 9 inches. How far does it travel in one rotation?

One rotation covers a distance equal to the circumference:

$C = 2\pi r = 2\pi(9) = 18\pi \approx 56.55 \text{ in}$

Answer: The wheel travels approximately 56.55 inches per rotation.

Perimeter Formula Reference

Real-World Application: Carpentry — Ordering Baseboard Trim

A carpenter is installing baseboard trim around a rectangular room that measures 16 ft by 12 ft. The room has one doorway that is 3 ft wide (no trim needed there). How many feet of baseboard should the carpenter buy?

Step 1: Calculate the full perimeter of the room.

$P = 2(16) + 2(12) = 32 + 24 = 56 \text{ ft}$

Step 2: Subtract the doorway opening.

$56 - 3 = 53 \text{ ft}$

Step 3: Add 10% for waste from cuts and fitting.

$53 \times 0.10 = 5.3 \text{ ft}$

$53 + 5.3 = 58.3 \text{ ft}$

Answer: The carpenter should order at least 59 feet of baseboard trim (rounding up, since trim is sold in whole lengths). Experienced carpenters always add a waste factor because each cut and corner produces a short piece that often cannot be reused.

Practice Problems

Test your understanding with these problems. Click to reveal each answer.

Key Takeaways

• Perimeter is the total distance around a shape, measured in linear units (ft, in, m — not square units)
• For rectangles: $P = 2l + 2w$. For squares: $P = 4s$. For triangles: add all three sides
• For any polygon, just add up all the side lengths
• A circle’s perimeter is called circumference: $C = 2\pi r = \pi d$
• In real-world applications, always account for openings (doors, windows) and add a waste factor when ordering materials

Return to Geometry for more topics in this section.