Perimeter of a Rectangle: Formula & Worked Examples

To calculate the perimeter of a rectangle, use the formula P = 2 × (length + width) or P = 2p + 2l. For example, a rectangle with a length of 12 cm and a width of 8 cm has a perimeter of 2 × (12 + 8) = 40 cm. The unit is always the same as the unit of the sides (cm, m, km).

What Is the Perimeter of a Rectangle

The perimeter of a rectangle is the total length of all the sides that surround it. The concept of perimeter has been used since ancient Egypt — Egyptian mathematicians around 1800 BCE used it to measure farmland along the Nile. A rectangle has two pairs of parallel sides of equal length:

• Length (p): the longer side
• Width (l): the shorter side

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Formula for the Perimeter of a Rectangle

In words: P = 2 × (length + width)

From this formula, we can also find an unknown side:

💡 Quick tip: Perimeter = (length + width) × 2. Just add one long side and one short side, then multiply by 2. Faster than adding all four sides one by one.

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How to Calculate the Perimeter of a Rectangle: Worked Examples

Example 1: Finding the Perimeter

A rectangle has a length of 12 cm and a width of 8 cm. Calculate its perimeter.

Step 1: Given p = 12 cm, l = 8 cm.

Step 2: Plug into the formula:

Answer: Perimeter of the rectangle = 40 cm

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Example 2: Finding the Width from the Perimeter

A rectangle has a perimeter of 36 cm and a length of 11 cm. What is its width?

Step 1: Use the formula l = P/2 − p:

Answer: Width of the rectangle = 7 cm

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Example 3: Word Problem

Pak Ahmad's garden in Bandung is rectangular, with a length of 25 m and a width of 15 m. How long a fence does he need to enclose the whole garden?

Step 1: p = 25 m, l = 15 m.

Answer: The fence needed is 80 m long.

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Common Mistakes When Calculating the Perimeter of a Rectangle

Mistake 1: Adding only two sides instead of four. Many students in grades 3–4 add p + l without multiplying by 2. Wrong: P = 12 + 8 = 20 cm (correct: P = 2 × 20 = 40 cm). Remember: a rectangle has four sides — two lengths and two widths, so the result is always multiplied by 2.

Mistake 2: Finding the width without dividing the perimeter by 2 first. If P = 36 cm and p = 11 cm, the common mistake is l = 36 − 11 = 25 cm. Correct: l = (P ÷ 2) − p = 18 − 11 = 7 cm. Always divide the perimeter by 2 before subtracting the known side.

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Perimeter of a Rectangle Table

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Practice Problems

Problem 1: ⭐ A rectangle with p = 14 cm and l = 9 cm. Calculate its perimeter.

Problem 2: ⭐⭐ A rectangle has a perimeter of 50 cm and a length of 15 cm. What is its width?

Problem 3: ⭐⭐⭐ A football pitch in Jakarta is rectangular, with a length of 90 m and a width of 60 m. How long is the touchline that goes around it?

Answer Key:

1. P = 2(14+9) = 2 × 23 = 46 cm
2. l = 50/2 − 15 = 25 − 15 = 10 cm
3. P = 2(90+60) = 2 × 150 = 300 m

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Summary

1. The perimeter of a rectangle is the total length of its four sides, calculated as P = 2(p + l).
2. A rectangle has two pairs of equal sides: two lengths (p) and two widths (l).
3. To find a side from a known perimeter: p = P/2 − l or l = P/2 − p.
4. The unit of perimeter is the same as the unit of the sides (cm, m, km).
5. Perimeter is used in real life to work out the length of fences, picture frames, or the touchline of a pitch.

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Read also: How to Calculate the Perimeter of a Circle and How to Find the Area of a Triangle.