Perimeter Formula: How to Find Perimeter of Any Shape

The perimeter of a two-dimensional shape is the total distance around its outside boundary. The basic perimeter formula is simple: add the lengths of all the outer sides. For shapes with equal or repeated sides, a shortcut formula makes the calculation faster. For example, a square uses (P=4s), a rectangle uses (P=2(l+w)), and a triangle uses (P=a+b+c). A circle is a special case because its perimeter is called circumference, calculated with (C=2\pi r) or (C=\pi d).

This guide explains how to find perimeter, gives the most useful perimeter formulas for common shapes, works through examples step by step, and explains the difference between perimeter and area.

What Is Perimeter?

Perimeter is the total length of the outside boundary of a two-dimensional shape. Another simple way to think about perimeter is to imagine walking once around the edge of a shape. The distance you travel is its perimeter.

For a polygon, the perimeter is found by adding the lengths of all its sides:

P = sum of all outside side lengths

Perimeter is a measurement of length, so the answer uses linear units such as centimeters (cm), meters (m), inches (in), feet (ft), or yards (yd). It does not use square units such as cm² or m².

Perimeter Explorer

Use the interactive explorer below to change the side lengths and see how the perimeter changes.

Perimeter vs. Area

Perimeter and area are related, but they measure different things.

A useful memory trick is: perimeter goes around, area goes inside.

How to Find Perimeter

For most perimeter problems, you can use the same basic process.

Step 1: Identify the shape

Look at the figure and determine whether it is a square, rectangle, triangle, regular polygon, or another shape.

Step 2: Find the length of every outside side

Check the labels carefully. If some sides are equal, use the information given by the shape.

For example, a rectangle has two pairs of equal opposite sides. A square has four equal sides.

Step 3: Add the outside side lengths

You can either add each side separately or use a shortcut perimeter formula for the shape.

Step 4: Check the units

Because perimeter measures length, your final answer should use a linear unit such as cm, m, ft, or in.

Example: A rectangle has a length of 8 cm and a width of 5 cm.
P=8+5+8+5
P=26 cm

Or use the shortcut:
P=2(8+5)=26 cm

This four-step approach works for most elementary and middle-school perimeter problems.

Perimeter Formulas for Common Shapes

The most important idea is that every polygon’s perimeter comes from adding its outside sides. The named formulas below are shortcuts based on equal or repeated side lengths.

Square Perimeter Formula

A square has four equal sides. Therefore:
P=4s

If each side is 7 cm:
P=4(7)=28 cm

Rectangle Perimeter Formula

A rectangle has two equal lengths and two equal widths:
P=2(l+w)

For a rectangle that is 10 m long and 4 m wide:
P=2(10+4)=28 m

Triangle Perimeter Formula

A triangle has three sides, so simply add them:
P=a+b+c

For side lengths of 6 cm, 8 cm, and 10 cm:
P=6+8+10=24 cm

This works for scalene, isosceles, equilateral, and right triangles as long as the three side lengths are known.

Parallelogram Perimeter Formula

A parallelogram has two pairs of equal opposite sides. If its adjacent sides are (a) and (b):
P=2(a+b)

For example, if the adjacent sides are 12 cm and 5 cm:
P=2(12+5)=34 cm

Important: The height is not used directly in the perimeter formula. Height is commonly used for finding the area of a parallelogram, not its perimeter.

Trapezoid Perimeter Formula

A trapezoid has four sides, so its perimeter is:
P=a+b+c+d

If its four side lengths are 8 cm, 5 cm, 6 cm, and 7 cm:
P=8+5+6+7=26 cm

The height of a trapezoid is not part of its perimeter formula unless the height is first used to determine an unknown side.

Regular Polygon Perimeter Formula

A regular polygon has equal side lengths. Therefore:
P=ns

where (n) is the number of sides and (s) is the length of one side.

For a regular pentagon with sides of 4 cm:
P=5(4)=20 cm

Circle Perimeter: Circumference

A circle does not have straight sides, so its perimeter has a special name: circumference.

If the radius is known:
C=2\pi r

If the diameter is known:
C=\pi d

For a circle with a diameter of 10 cm:
C=\pi(10)\approx31.42 cm

Remember that (d=2r), so both formulas give the same result.

Perimeter Examples: Step-by-Step

Example 1: Find the Perimeter of a Square

A square has a side length of 9 inches. What is its perimeter?

Step 1: Identify the formula.
P=4s

Step 2: Substitute the side length.
P=4(9)

Step 3: Calculate.
P=36 in

Answer: 36 inches

Example 2: Find the Perimeter of a Rectangle

A rectangle is 12 ft long and 7 ft wide.
P=2(l+w)
P=2(12+7)
P=2(19)=38 ft

Answer: 38 feet

Example 3: Find the Perimeter of a Triangle

A triangle has sides of 5 m, 7 m, and 9 m.
P=a+b+c
P=5+7+9
P=21 m

Answer: 21 meters

Example 4: Find a Missing Side

A triangle has a perimeter of 30 cm. Two sides are 8 cm and 11 cm. What is the third side?

Start with the triangle perimeter formula:
30=8+11+x
30=19+x
x=11

Answer: The missing side is 11 cm.

This method can be used whenever the perimeter and enough other side lengths are known.

Example 5: Find the Perimeter of an Irregular Polygon

Suppose an irregular polygon has outside side lengths of 4 cm, 7 cm, 3 cm, 6 cm, and 5 cm.

Add every outside side:
P=4+7+3+6+5
P=25 cm

The key is to trace the entire outside boundary once. Do not add interior lines that do not form part of the boundary.

FAQ

1. How to find perimeter?

To find perimeter, add the lengths of all the outside sides of a two-dimensional shape. For shapes with equal sides, you can use a shortcut formula. For example, use (P=4s) for a square and (P=2(l+w)) for a rectangle. Always write the answer using a linear unit such as cm, m, ft, or in.

2. What is perimeter?

Perimeter is the total distance around the outside boundary of a two-dimensional shape. For a polygon, it is the sum of all its side lengths. Perimeter measures length, so it is expressed in units such as centimeters, meters, inches, or feet.

3. How to find the perimeter of a triangle?

To find the perimeter of a triangle, add the lengths of all three sides:
P=a+b+c

For example, a triangle with sides of 5 cm, 7 cm, and 9 cm has:
P=5+7+9=21 cm

For an equilateral triangle, all three sides are equal, so the shortcut is (P=3s).

4. What is the perimeter formula for a rectangle?

The perimeter formula for a rectangle is:
P=2(l+w)

where (l) is the length and (w) is the width. The formula works because a rectangle has two equal lengths and two equal widths.

5. What is the difference between perimeter and area?

Perimeter measures the distance around the outside of a shape, while area measures the amount of space inside it. Perimeter uses linear units such as cm and m. Area uses square units such as cm² and m².

Conclusion

The perimeter formula helps you measure the complete distance around a two-dimensional shape. The most important rule is simple: add the lengths of all the outside sides. Shortcut formulas make this faster for familiar shapes, such as (P=4s) for a square, (P=2(l+w)) for a rectangle, (P=a+b+c) for a triangle, and (P=ns) for a regular polygon. For circles, the perimeter is called circumference and can be found with (C=2\pi r) or (C=\pi d).

For students who want more guided practice with geometry and other core math skills, WuKong Math provides online math class for kids designed to build mathematical understanding step by step.

Delvair | WuKong Math Teacher

Delvair, a graduate of the Federal University of Maranhão in Brazil, is a dedicated educator with over six years of experience in school-based mathematics instruction. She specializes in advanced math pedagogy, with a particular expertise in Math Kangaroo competition coaching. Driven by the belief that education is the bedrock of a thriving society, Delvair is committed to creating an empowering environment where every child can excel. She holds the firm conviction that with the right guidance, every student possesses the potential to master complex mathematical concepts.