Complete Guide to Perimeter of Polygon Examples for 3rd Grade

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

Perimeter Examples Solutions
1 Rectangle perimeter
Example 1
A rectangle has a length of 8 cm and a width of 5 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 = 8, w = 5
Formula
P = 2(l+w)
Calculate
P = 26 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(8 + 5)

Step 3: Calculate

P = 2(13) = 26

Step 4: Include unit

The perimeter is 26 cm.

Perimeter = 26 cm
Final answer:

The perimeter of the rectangle is 26 cm.

Applied rules:

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

• Addition: Add length and width first

• Multiplication: Multiply by 2

2 Square perimeter
Example 2
A square has sides of 6 cm. What is its perimeter?
Definition:

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

Given
side = 6 cm
Formula
P = 4s
Calculate
P = 24 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(6)

Step 3: Calculate

P = 24

Step 4: Include unit

The perimeter is 24 cm.

Perimeter = 24 cm
Final answer:

The perimeter of the square is 24 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
Example 3
A triangle has sides of 4 cm, 6 cm, and 7 cm. What is its perimeter?
Definition:

Triangle Perimeter: Sum of all three sides. P = a + b + c

Given
a = 4, b = 6, c = 7
Formula
P = a + b + c
Calculate
P = 17 cm
Step 1: Write the perimeter formula for a triangle

For a triangle: Perimeter = side₁ + side₂ + side₃

P = a + b + c

Step 2: Substitute known values

P = 4 + 6 + 7

Step 3: Calculate

P = 17

Step 4: Include unit

The perimeter is 17 cm.

Perimeter = 17 cm
Final answer:

The perimeter of the triangle is 17 cm.

Applied rules:

• Triangle perimeter formula: Sum of all three sides

• Addition: Add all three side lengths

• Verification: Check that you added all sides

More Perimeter Examples
Example Set A
Example A1: A rectangle has a length of 10 cm and a width of 4 cm. Find its perimeter.
Example A2: A square has sides of 5 cm. Find its perimeter.
Example A3: A triangle has sides of 3 cm, 4 cm, and 5 cm. Find its perimeter.
Example Set B
Example B1: A rectangle has a length of 12 cm and a width of 7 cm. Find its perimeter.
Example B2: A square has sides of 8 cm. Find its perimeter.
Example B3: A triangle has sides of 6 cm, 8 cm, and 10 cm. Find its perimeter.
▭
Rectangle
P = 2(l + w)

Perimeter = 2(length + width)

□
Square
P = 4s

Perimeter = 4 × side

△
Triangle
P = a + b + c

Perimeter = sum of sides

⬟
Polygon
P = sum of sides

Add all sides

Rectangle: P = 2(l + w)
Rectangle Perimeter
Square
P = 4s
All sides equal
Triangle
P = a + b + c
Sum of sides
Any Polygon
P = sum of all sides
Add all lengths
Problem-Solving Steps:
  1. Identify the shape and its perimeter formula
  2. List known values and identify what's unknown
  3. Set up the equation using the perimeter formula
  4. Solve for the unknown using algebraic methods
  5. Verify your answer by substituting back
Advanced Perimeter Examples
4 Pentagon perimeter
Example 4
A regular pentagon has sides of 5 cm. Find its perimeter.
Definition:

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

Given
side = 5 cm
Formula
P = 5s
Calculate
P = 25 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(5)

Step 3: Calculate

P = 25

Step 4: Include unit

The perimeter is 25 cm.

Perimeter = 25 cm
Final answer:

The perimeter of the pentagon is 25 cm.

5 Hexagon perimeter
Example 5
A regular hexagon has sides of 7 cm. Find its perimeter.
Definition:

Regular Hexagon: A six-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 Polygon Examples

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.

Polygon: Any shape made up of straight lines. Examples: triangle, rectangle, square, pentagon, 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.

Regular Polygon: A polygon where all sides and angles are equal.

Core Rules and Principles:

• Perimeter Rule: Perimeter = sum of all side lengths

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

• Square Perimeter: P = 4 × side length

• Triangle Perimeter: P = side₁ + side₂ + side₃

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

Step-by-Step Method:
  1. Identify the shape: Determine if it's a rectangle, square, triangle, etc.
  2. Count the sides: Know how many sides the shape has
  3. Measure or get side lengths: Find the length of each side
  4. Add all side lengths: Sum them up to get the perimeter
  5. State the answer: Include the unit (cm, m, inches, etc.)
Perimeter Example: Rectangle

Rectangle with length = 6 cm and width = 4 cm

Step 1: P = 2(l + w) = 2(6 + 4) = 2(10) = 20 cm

Step 2: The perimeter is 20 cm

Perimeter Example: Square

Square with side = 5 cm

Step 1: P = 4s = 4(5) = 20 cm

Step 2: The perimeter is 20 cm

Perimeter Example: Triangle

Triangle with sides = 3 cm, 4 cm, 5 cm

Step 1: P = a + b + c = 3 + 4 + 5 = 12 cm

Step 2: The perimeter is 12 cm

Perimeter Example: Regular Pentagon

Regular pentagon with side = 4 cm

Step 1: P = 5s = 5(4) = 20 cm

Step 2: The perimeter is 20 cm

Memory Tip 1: "Perimeter" sounds like "fence-meter" - you measure the fence around a yard!
Memory Tip 2: Rectangle has 2 lengths and 2 widths, so P = 2(l + w).
Memory Tip 3: Square has 4 equal sides, so P = 4s.
Common Mistake: Don't forget that rectangles have 2 pairs of equal sides.
Common Mistake: Always check your answer by recalculating the perimeter.
Key Takeaways: 1) Always identify the shape first, 2) Use the correct formula, 3) Check your work by substituting back.
Real World Application: Useful for measuring fences, borders, frames, and edges of objects.
Perimeter Examples and Formulas
P = sum of all sides
Universal Perimeter Formula
Perimeter Examples:

Rectangle: P = 2(l + w) where l = length, w = width

Square: P = 4s where s = side length

Triangle: P = a + b + c where a, b, c are side lengths

Regular Pentagon: P = 5s where s = side length

Regular Hexagon: P = 6s where s = side length

Regular Polygon: P = n × s where n = number of sides, s = side length

Complete methodology:
  1. Identify the shape: Recognize whether it's a rectangle, square, triangle, etc.
  2. Select the formula: Use the appropriate perimeter formula
  3. Substitute known values: Fill in the given measurements
  4. Solve for unknown: Use algebraic operations to find missing side
  5. Verify solution: Check that your answer makes sense
Tip 1: Always label your sides clearly to avoid confusion.
Tip 2: Remember that rectangles have 2 pairs of equal sides.
Tip 3: Draw the shape and label known sides to visualize the problem.
Tip 4: Always check your answer by calculating the perimeter with your solution.
Common errors: Forgetting that rectangles have 2 lengths and 2 widths, miscounting sides, arithmetic mistakes.
Key formulas: Rectangle: P=2(l+w), Square: P=4s, Triangle: P=a+b+c
Essential rules to remember:

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

• Square rule: P = 4 × side length

• Triangle rule: P = side₁ + side₂ + side₃

• 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+4+5=12
Practical 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", "unknown side"
  4. Write what you know: List given information
  5. Write what you need: Identify the unknown
  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
  • General: "Perimeter means add all sides"

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)

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