Complete Perimeter of Regular Polygon Worksheet for 3rd Grade

Master calculating perimeter of rectangles, squares, and regular polygons with detailed worksheets and solutions.

Worksheet Solutions: Perimeter Exercises
1 Rectangle perimeter
Worksheet 1
A rectangle has a length of 10 cm and a width of 7 cm. What is its perimeter?
Definition:

Perimeter: The total distance around the outside of a shape. For a rectangle: P = 2 × (length + width)

Method:
  1. Write the perimeter formula for a rectangle
  2. Substitute known values
  3. Calculate the result
  4. Include the unit
Given
l = 10, w = 7
Formula
P = 2(l+w)
Calculate
P = 34 cm
Step 1: Write the perimeter formula

For a rectangle: Perimeter = 2 × (length + width)

P = 2(l + w)

Step 2: Substitute known values

P = 2(10 + 7)

Step 3: Calculate

P = 2(17) = 34

Step 4: Include unit

The perimeter is 34 cm.

Perimeter = 34 cm
Final answer:

The perimeter of the rectangle is 34 cm.

Applied rules:

• Rectangle perimeter formula: P = 2(l + w)

• Addition: Add length and width first

• Multiplication: Multiply by 2

2 Square perimeter
Worksheet 2
A square has sides of 8 cm. What is its perimeter?
Definition:

Square Perimeter: Since all sides are equal, P = 4 × side length

Given
side = 8 cm
Formula
P = 4s
Calculate
P = 32 cm
Step 1: Write the perimeter formula for a square

For a square: Perimeter = 4 × side length

P = 4s

Step 2: Substitute the side length

P = 4(8)

Step 3: Calculate

P = 32

Step 4: Include unit

The perimeter is 32 cm.

Perimeter = 32 cm
Final answer:

The perimeter of the square is 32 cm.

Applied rules:

• Square perimeter formula: P = 4s

• All sides equal: In a square, all four sides are the same length

• Multiplication: Multiply side length by 4

3 Triangle perimeter
Worksheet 3
An equilateral triangle has sides of 6 cm. What is its perimeter?
Definition:

Regular Triangle (Equilateral): A 3-sided shape with all sides equal. P = 3 × side length

Given
side = 6 cm
Formula
P = 3s
Calculate
P = 18 cm
Step 1: Write the perimeter formula for an equilateral triangle

For an equilateral triangle: Perimeter = 3 × side length

P = 3s

Step 2: Substitute the side length

P = 3(6)

Step 3: Calculate

P = 18

Step 4: Include unit

The perimeter is 18 cm.

Perimeter = 18 cm
Final answer:

The perimeter of the equilateral triangle is 18 cm.

Applied rules:

• Equilateral triangle perimeter: P = 3s

• All sides equal: In an equilateral triangle, all three sides are the same length

• Multiplication: Multiply side length by 3

Regular Polygon Worksheet Problems
Problem Set A
Problem A1: A rectangle has a perimeter of 36 cm. If one side is 10 cm, find the other side.
Problem A2: A square has a perimeter of 32 cm. What is each side length?
Problem A3: A triangle has sides of 5 cm, 6 cm, and 7 cm. What is its perimeter?
Problem Set B
Problem B1: A rectangle has a perimeter of 44 cm. If the length is 14 cm, what is the width?
Problem B2: A regular pentagon has sides of 5 cm. What is its perimeter?
Problem B3: A square garden has a perimeter of 48 meters. How long is each side?
▭
Rectangle
P = 2(l + w)
4 sides
□
Square
P = 4s
4 equal sides
△
Triangle
P = 3s
3 sides
⬟
Pentagon
P = 5s
5 sides
.Hexagon
Hexagon
P = 6s
6 sides
Octagon
Octagon
P = 8s
8 sides
Regular Polygon: P = n × s
Where n = number of sides, s = side length
Rectangle
P = 2(l + w)
Opposite sides equal
Square
P = 4s
All sides equal
Triangle
P = 3s
Equilateral triangle
Any Regular Polygon
P = n × s
n = number of sides
Problem-Solving Steps:
  1. Identify the shape: Determine if it's a rectangle, square, triangle, etc.
  2. Count the sides: Know how many sides the polygon has
  3. Select the formula: Use the appropriate perimeter formula
  4. Substitute values: Fill in the known measurements
  5. Calculate: Perform the arithmetic operations
  6. Include unit: Add the measurement unit (cm, m, inches)
Advanced Polygon Worksheet Exercises
4 Pentagon perimeter
Worksheet 4
A regular pentagon has sides of 6 cm. What is its perimeter?
Definition:

Regular Pentagon: A 5-sided shape with all sides equal. P = 5 × side length

Given
side = 6 cm
Formula
P = 5s
Calculate
P = 30 cm
Step 1: Write the perimeter formula for a regular pentagon

For a regular pentagon: Perimeter = 5 × side length

P = 5s

Step 2: Substitute the side length

P = 5(6)

Step 3: Calculate

P = 30

Step 4: Include unit

The perimeter is 30 cm.

Perimeter = 30 cm
Final answer:

The perimeter of the pentagon is 30 cm.

5 Hexagon perimeter
Worksheet 5
A regular hexagon has sides of 7 cm. What is its perimeter?
Definition:

Regular Hexagon: A 6-sided shape with all sides equal. P = 6 × side length

Given
side = 7 cm
Formula
P = 6s
Calculate
P = 42 cm
Step 1: Write the perimeter formula for a regular hexagon

For a regular hexagon: Perimeter = 6 × side length

P = 6s

Step 2: Substitute the side length

P = 6(7)

Step 3: Calculate

P = 42

Step 4: Include unit

The perimeter is 42 cm.

Perimeter = 42 cm
Final answer:

The perimeter of the hexagon is 42 cm.

Complete Summary: Perimeter of Regular Polygons

Key Concepts and Definitions:

Perimeter: The total distance around the outside of a 2D shape. It's like walking all the way around the edge of the shape.

Regular Polygon: A polygon where all sides and angles are equal. Examples: equilateral triangle, square, regular pentagon, regular hexagon.

Rectangle: A 4-sided shape where opposite sides are equal and all angles are 90°.

Square: A special rectangle where all 4 sides are equal.

Equilateral Triangle: A triangle where all 3 sides are equal.

Regular Pentagon: A 5-sided shape where all sides are equal.

Regular Hexagon: A 6-sided shape where all sides are equal.

Core Rules and Principles:

• Perimeter Rule: Perimeter = sum of all side lengths

• Rectangle Rule: P = 2(length + width)

• Square Rule: P = 4 × side length

• Equilateral Triangle Rule: P = 3 × side length

• Regular Polygon Rule: P = number of sides × side length

Step-by-Step Method for Regular Polygons:
  1. Count the sides: Determine how many sides the polygon has (n)
  2. Measure or get side length: Find the length of each equal side (s)
  3. Apply the formula: P = n × s
  4. Calculate: Multiply the number of sides by the side length
  5. Include unit: Add the measurement unit (cm, m, inches, etc.)
Perimeter Example: Rectangle

Rectangle with length = 8 cm and width = 5 cm

Step 1: P = 2(l + w) = 2(8 + 5) = 2(13) = 26 cm

Step 2: The perimeter is 26 cm

Perimeter Example: Square

Square with side = 6 cm

Step 1: P = 4s = 4(6) = 24 cm

Step 2: The perimeter is 24 cm

Perimeter Example: Regular Pentagon

Regular pentagon with side = 5 cm

Step 1: P = 5s = 5(5) = 25 cm

Step 2: The perimeter is 25 cm

Perimeter Example: Regular Hexagon

Regular hexagon with side = 4 cm

Step 1: P = 6s = 6(4) = 24 cm

Step 2: The perimeter is 24 cm

Memory Tip 1: "Perimeter" sounds like "fence-meter" - you measure the fence around a yard!
Memory Tip 2: For regular polygons: P = number of sides × side length.
Memory Tip 3: Square has 4 equal sides → P = 4s.
Common Mistake: Don't forget that rectangles have 2 lengths and 2 widths.
Common Mistake: Always include units in your answer (cm, m, inches, etc.)
Key Takeaways: 1) Regular polygons have all sides equal, 2) Use P = n × s, 3) Count sides carefully.
Real World Application: Useful for measuring fences, borders, frames, and edges of objects.
Worksheet Answer Key
P = sum of all sides
Universal Perimeter Formula
Regular Polygon: P = n × s
Where n = number of sides, s = side length
Key definitions:

Perimeter: The total distance around the edge of a 2D shape

Rectangle: A 4-sided shape with opposite sides equal and all angles 90°

Square: A 4-sided shape with all sides equal and all angles 90°

Triangle: A 3-sided polygon

Regular Polygon: A polygon with all sides and angles equal

Complete methodology:
  1. Identify the shape: Recognize whether it's a rectangle, square, triangle, etc.
  2. Count the sides: Know how many sides the polygon has
  3. Select the formula: Use the appropriate perimeter formula
  4. Substitute known values: Fill in the given measurements
  5. Calculate: Perform the necessary arithmetic operations
  6. Include unit: Add the measurement unit (cm, m, inches)
Tip 1: Always count the sides carefully to determine the number of sides (n).
Tip 2: Remember that in regular polygons, all sides are equal.
Tip 3: Draw the shape and label known sides to visualize the problem.
Tip 4: Always check your answer by verifying the number of sides and side length.
Common errors: Miscounting sides, forgetting that rectangles have 2 lengths and 2 widths, arithmetic mistakes.
Key formulas: Rectangle: P=2(l+w), Square: P=4s, Regular Polygon: P=n×s
Essential rules to remember:

• Rectangle rule: P = 2(length + width)

• Square rule: P = 4 × side length

• Equilateral triangle rule: P = 3 × side length

• Regular polygon rule: P = number of sides × side length

• General rule: P = sum of all side lengths

Examples: P=2(5+3)=16, P=4(5)=20, P=3(6)=18, P=5(4)=20
Formula Applications

Questions & Answers

Question: I'm confused about why we multiply by 2 in the rectangle perimeter formula. Why isn't it just length + width?

Answer: Great question! When we calculate perimeter, we need to count ALL the sides of the rectangle. A rectangle has 4 sides:

  • One length side
  • One width side
  • Another length side (opposite to the first)
  • Another width side (opposite to the first)

So we have: length + width + length + width = 2×length + 2×width = 2(length + width)

Think of walking around the rectangle - you travel the length twice and the width twice!

Example: If length = 5 and width = 3, the perimeter is 5+3+5+3 = 16, which equals 2(5+3) = 16.

Question: My child is struggling with word problems involving perimeter. How can I help them identify what's being asked?

Answer: Here's a helpful strategy to teach your child:

  1. Read carefully: Have them read the problem multiple times
  2. Draw a picture: Sketch the shape and label known sides
  3. Circle key words: Look for "perimeter", "around", "distance", "total", "fence", "border"
  4. Write what you know: List given information
  5. Write what you need: Identify what's being asked
  6. Choose the formula: Select the correct perimeter formula
  7. Solve step by step: Show work clearly

Practice with real-world examples: "If you want to put a fence around a rectangular garden, how much fencing do you need?" connects perimeter to practical situations.

Question: Are there any memory tricks to remember the different perimeter formulas for various shapes?

Answer: Yes! Here are some effective memory tricks:

  • Rectangle: "Two lengths, two widths" → P = 2(l + w)
  • Square: "Four equal sides" → P = 4s
  • Triangle: "Three sides to add" → P = a + b + c
  • Regular Polygon: "Number of sides times side length" → P = n × s

Visual memory trick: Draw the shapes and write the number of sides next to each:
Rectangle (4 sides, opposite pairs equal)
Square (4 sides, all equal)
Triangle (3 sides)
Pentagon (5 sides)
Hexagon (6 sides)

Physical activity: Walk around the perimeter of different shaped objects while counting the sides out loud.