Perimeter of Regular Polygons Worksheet - Complete Guide

Master perimeter calculations for regular polygons: triangles, squares, pentagons, hexagons, and more with detailed exercises and solutions.

Exercise Solutions 1 to 3
1 Square Perimeter
Exercise 1
A square has sides of length 5 cm. What is its perimeter?
Definition:

Regular polygon: A shape with all sides equal and all angles equal

Square: A regular polygon with 4 equal sides and 4 right angles

Perimeter: The total distance around the outside of a shape

Method for Regular Polygons:
  1. Count the number of sides (n)
  2. Measure the length of one side (s)
  3. Multiply: Perimeter = n × s
Square
4 sides
Side Length
5 cm
Perimeter
4 × 5 = 20 cm
Step 1: Identify the polygon

A square has 4 equal sides

Step 2: Measure one side

Each side = 5 cm

Step 3: Apply the formula

Perimeter = Number of sides × Side length

Perimeter = 4 × 5 = 20 cm

Step 4: Verify the calculation

5 + 5 + 5 + 5 = 20 cm ✓

Perimeter = 20 cm
Final answer:

The perimeter of the square is 20 cm

Applied rules:

• Regular Polygon Rule: All sides are equal

• Perimeter Formula: P = n × s where n = number of sides, s = side length

• Verification: Add all sides to confirm result

Tip: For a square, multiply side length by 4 to get perimeter.
2 Hexagon Perimeter
Exercise 2
A regular hexagon has sides of length 6 cm. What is its perimeter?
Definition:

Regular hexagon: A six-sided polygon with all sides and angles equal

Hexagon: Has 6 sides

Hexagon
6 sides
Side Length
6 cm
Perimeter
6 × 6 = 36 cm
Step 1: Count the sides

A hexagon has 6 sides

Step 2: Measure one side

Each side = 6 cm

Step 3: Apply the formula

Perimeter = 6 × 6 = 36 cm

Step 4: Verify

6 + 6 + 6 + 6 + 6 + 6 = 36 cm ✓

Perimeter = 36 cm
Final answer:

The perimeter of the hexagon is 36 cm

Applied rules:

• Regular Polygon Rule: All sides are equal

• Perimeter Formula: P = n × s

• Hexagon Property: Has 6 equal sides

Tip: For any regular polygon, multiply the number of sides by the side length.
3 Triangle Perimeter
Exercise 3
An equilateral triangle has sides of length 7 cm. What is its perimeter?
Definition:

Equilateral triangle: A regular triangle with all 3 sides equal

Triangle: Has 3 sides

Triangle
3 sides
Side Length
7 cm
Perimeter
3 × 7 = 21 cm
Step 1: Identify the polygon

An equilateral triangle has 3 equal sides

Step 2: Measure one side

Each side = 7 cm

Step 3: Apply the formula

Perimeter = 3 × 7 = 21 cm

Step 4: Verify

7 + 7 + 7 = 21 cm ✓

Perimeter = 21 cm
Final answer:

The perimeter of the triangle is 21 cm

Applied rules:

• Regular Polygon Rule: All sides are equal

• Perimeter Formula: P = n × s

• Triangle Property: Has 3 sides

Tip: For an equilateral triangle, multiply the side length by 3.
Key Formulas, Definitions & Properties
P = n × s
Perimeter of Regular Polygon
Key Definitions:

Regular Polygon: A shape with all sides equal and all angles equal

Perimeter: The total distance around the outside of a shape

Side Length (s): The measurement of one side of the polygon

Number of Sides (n): The count of sides in the polygon

Triangle
P = 3s
3 sides
Square
P = 4s
4 sides
Pentagon
P = 5s
5 sides
Hexagon
P = 6s
6 sides
Regular Polygon Properties: All sides equal, all angles equal, symmetry
Perimeter Calculation: Count sides × measure one side
Tip 1: Count the sides carefully to identify the polygon.
Tip 2: Measure one side accurately since all sides are equal.
Tip 3: Always verify by adding all sides together.
Tip 4: Remember: P = n × s works for ALL regular polygons.
Advanced Examples & Practice
4 Pentagon Perimeter
Exercise 4
A regular pentagon has sides of length 4 cm. What is its perimeter?
Definition:

Regular pentagon: A five-sided polygon with all sides and angles equal

Pentagon
5 sides
Side Length
4 cm
Perimeter
5 × 4 = 20 cm
Step 1: Identify the polygon

A pentagon has 5 sides

Step 2: Measure one side

Each side = 4 cm

Step 3: Apply the formula

Perimeter = 5 × 4 = 20 cm

Perimeter = 20 cm
Final answer:

The perimeter of the pentagon is 20 cm

Applied rules:

• Regular Polygon Formula: P = n × s

• Pentagon Property: Has 5 equal sides

5 Octagon Perimeter
Exercise 5
A regular octagon has sides of length 3 cm. What is its perimeter?
Definition:

Regular octagon: An eight-sided polygon with all sides and angles equal

Octagon
8 sides
Side Length
3 cm
Perimeter
8 × 3 = 24 cm
Step 1: Identify the polygon

An octagon has 8 sides

Step 2: Measure one side

Each side = 3 cm

Step 3: Apply the formula

Perimeter = 8 × 3 = 24 cm

Perimeter = 24 cm
Final answer:

The perimeter of the octagon is 24 cm

Applied rules:

• Regular Polygon Formula: P = n × s

• Octagon Property: Has 8 equal sides

Complete Learning Guide: Perimeter of Regular Polygons
P = n × s
Perimeter Formula
Key definitions:

Regular Polygon: A shape with all sides equal and all angles equal

Perimeter: The total distance around the outside of a shape

Side Length (s): The measurement of one side of the polygon

Number of Sides (n): The count of sides in the polygon

Complete methodology:
  1. Identify the polygon: Count the number of sides (triangle, square, pentagon, etc.)
  2. Measure one side: Since all sides are equal, measuring one gives all measurements
  3. Apply the formula: Perimeter = Number of sides × Side length
  4. Verify the result: Add all sides to confirm the calculation
Triangle
P = 3s
3 sides
Square
P = 4s
4 sides
Pentagon
P = 5s
5 sides
Hexagon
P = 6s
6 sides
Heptagon
P = 7s
7 sides
Octagon
P = 8s
8 sides
Tip 1: Count sides carefully - a pentagon has 5, hexagon has 6, octagon has 8.
Tip 2: In regular polygons, all sides are equal, so measure just one.
Tip 3: Always verify by adding all sides: s₁ + s₂ + s₃ + ... = Perimeter.
Tip 4: Remember the general formula: Perimeter = n × s (number of sides × side length).
Common errors: Counting sides incorrectly, forgetting that all sides are equal, miscalculating multiplication.
Exam preparation: Memorize names of polygons, practice counting sides, master the P = n × s formula.
Key formulas to remember:

• General formula: P = n × s

• Triangle: P = 3s

• Square: P = 4s

• Pentagon: P = 5s

• Hexagon: P = 6s

• Heptagon: P = 7s

• Octagon: P = 8s

Questions & Answers

Question: I'm confused about regular polygons. What makes a polygon "regular" and why does this matter for calculating perimeter?

Answer: Great question! A "regular" polygon has two important properties:

  • All sides are equal in length
  • All angles are equal in measure

This matters for perimeter because:

  • If all sides are equal, you only need to measure one side
  • Then multiply by the number of sides: P = n × s
  • This makes calculations much simpler than irregular shapes

For example, in a regular hexagon with side length 5 cm: Instead of adding 5 + 5 + 5 + 5 + 5 + 5, you can calculate 6 × 5 = 30 cm

Question: My child is struggling to remember the names of polygons. Are there any tricks to help them learn them?

Answer: Yes, here are some helpful memory tricks for polygon names:

  • Tri-angle: Think "tricycle" (3 wheels) → Triangle has 3 sides
  • Square: Just remember it has 4 equal sides
  • Penta-gon: Think "Pentagon building" in Washington (5 sides)
  • Hexa-gon: "Hex" sounds like "six" → 6 sides
  • Hepta-gon: "Hept" sounds like "heaven" (7 days in a week)
  • Octa-gon: "Octopus" has 8 arms → 8 sides

You can also create flashcards with the number of sides drawn on one side and the polygon name on the other side.

Practice by drawing shapes and counting sides together!

Question: How can I help students verify their perimeter calculations to catch mistakes?

Answer: Here are effective verification strategies for students:

  • Add all sides: Have students add each individual side length to check against their multiplication result
  • Visual counting: On drawn shapes, count each side while saying the addition out loud
  • Estimation check: Does the answer make sense? A small square shouldn't have a huge perimeter
  • Reverse calculation: If perimeter is 20 and it's a square, each side should be 20 ÷ 4 = 5

Encourage students to always verify their work by using both multiplication (n × s) and addition (s + s + s...) to confirm they get the same result.

This builds good mathematical habits and increases confidence in their answers.