Complete Perimeter with Unknown Sides Worksheet for 3rd Grade

Master finding unknown sides of rectangles, squares, and polygons with detailed exercises and step-by-step solutions.

Worksheet Solutions: Exercises 1 to 3
1 Rectangle with unknown side
Exercise 1
A rectangle has a perimeter of 28 cm. One side measures 10 cm. What is the length of the unknown side?
Definition:

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

Method:
  1. Write the perimeter formula for a rectangle
  2. Substitute known values
  3. Solve for the unknown side
  4. Verify the answer
Given
P = 28, one side = 10
Formula
P = 2(l+w)
Unknown
w = ?
Step 1: Write the perimeter formula

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

P = 2(l + w)

Step 2: Substitute known values

28 = 2(10 + w)

Step 3: Solve for the unknown

Divide both sides by 2: 14 = 10 + w

Subtract 10 from both sides: 14 - 10 = w

w = 4

Step 4: Verify the answer

P = 2(10 + 4) = 2(14) = 28 ✓

The unknown side is 4 cm
Final answer:

The length of the unknown side is 4 cm.

Applied rules:

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

• Algebraic manipulation: Isolate the unknown variable

• Verification: Always check your answer by substituting back

2 Square with unknown side
Exercise 2
A square has a perimeter of 36 cm. What is the length of each side?
Definition:

Square: A four-sided shape where all sides are equal. P = 4 × side

Given
P = 36
Formula
P = 4s
Unknown
s = ?
Step 1: Write the perimeter formula for a square

For a square: Perimeter = 4 × side length

P = 4s

Step 2: Substitute the known perimeter

36 = 4s

Step 3: Solve for the side length

Divide both sides by 4: s = 36 ÷ 4

s = 9

Step 4: Verify the answer

P = 4(9) = 36 ✓

Each side is 9 cm
Final answer:

Each side of the square is 9 cm long.

Applied rules:

• Square perimeter formula: P = 4s

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

• Division: To find one side, divide the perimeter by 4

3 Triangle with unknown side
Exercise 3
A triangle has a perimeter of 24 cm. Two sides measure 7 cm and 10 cm. What is the length of the third side?
Definition:

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

Given
P = 24, a = 7, b = 10
Formula
P = a + b + c
Unknown
c = ?
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

24 = 7 + 10 + c

Step 3: Simplify and solve for the unknown

24 = 17 + c

c = 24 - 17

c = 7

Step 4: Verify the answer

P = 7 + 10 + 7 = 24 ✓

The third side is 7 cm
Final answer:

The length of the third side is 7 cm.

Applied rules:

• Triangle perimeter formula: Sum of all three sides

• Addition/Subtraction: Use inverse operations to isolate the unknown

• Verification: Check that all sides add up to the given perimeter

Additional Worksheet Problems
Problem Set A
Problem A1: A rectangle has a perimeter of 30 cm. If one side is 8 cm, find the other side.
Problem A2: A square has a perimeter of 28 cm. What is each side length?
Problem A3: A triangle has sides of 5 cm and 6 cm. If the perimeter is 18 cm, find the third side.
Problem Set B
Problem B1: A rectangle has a perimeter of 40 cm. If the length is 12 cm, what is the width?
Problem B2: A pentagon has sides of 4 cm, 5 cm, 6 cm, and 7 cm. If the perimeter is 30 cm, find the fifth side.
Problem B3: A square garden has a perimeter of 44 meters. How long is each side?
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 Worksheet Exercises
4 Irregular polygon
Exercise 4
A hexagon has a perimeter of 42 cm. Five sides measure 6 cm, 7 cm, 5 cm, 8 cm, and 9 cm. Find the sixth side.
Definition:

Irregular polygon: A shape with sides of different lengths. Perimeter = sum of all sides.

Given
P = 42, sides = 6,7,5,8,9
Formula
P = s₁+s₂+s₃+s₄+s₅+s₆
Unknown
s₆ = ?
Step 1: Write the perimeter formula

For a hexagon: P = s₁ + s₂ + s₃ + s₄ + s₅ + s₆

Step 2: Substitute known values

42 = 6 + 7 + 5 + 8 + 9 + s₆

Step 3: Simplify and solve

42 = 35 + s₆

s₆ = 42 - 35 = 7

Step 4: Verify

P = 6 + 7 + 5 + 8 + 9 + 7 = 42 ✓

Sixth side = 7 cm
Final answer:

The sixth side is 7 cm.

5 Rectangle with variables
Exercise 5
A rectangle has a perimeter of 44 cm. If one side is 6 cm longer than the other, find both sides.
Definition:

Algebraic approach: Use variables to represent unknown quantities and set up equations.

Let
w = x, l = x+6
Formula
P = 2(l+w)
Equation
44 = 2(x+x+6)
Step 1: Define variables

Let width = x, then length = x + 6

Step 2: Set up equation

44 = 2(x + (x + 6))

44 = 2(2x + 6)

Step 3: Solve

44 = 4x + 12

32 = 4x

x = 8

Step 4: Find both sides

Width = 8 cm, Length = 8 + 6 = 14 cm

Step 5: Verify

P = 2(8 + 14) = 2(22) = 44 ✓

Width = 8 cm, Length = 14 cm
Final answer:

The sides are 8 cm and 14 cm.

Complete Summary: Finding Perimeter with Unknown Sides

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.

Unknown side: A measurement we need to find when we know the perimeter and some other side lengths.

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.

Triangle: A 3-sided polygon.

Polygon: Any shape made up of straight lines.

Core Rules and Principles:

• Perimeter Rule: Perimeter = sum of all side lengths

• Rectangle Rule: P = 2(length + width) because opposite sides are equal

• Square Rule: P = 4 × side length because all sides are equal

• Triangle Rule: P = side₁ + side₂ + side₃

• Algebra Rule: Use inverse operations to solve for unknowns

Step-by-Step Method:
  1. Identify the shape: Determine if it's a rectangle, square, triangle, etc.
  2. Write the formula: Use the correct perimeter formula for the shape
  3. Substitute known values: Fill in the measurements you know
  4. Solve for the unknown: Use addition/subtraction or division to find the missing measurement
  5. Verify your answer: Plug your answer back into the formula to check
Simple Example: Rectangle

Rectangle with P = 20, one side = 7. Find unknown side.

Step 1: P = 2(l + w) → 20 = 2(7 + w)

Step 2: 20 = 14 + 2w → 6 = 2w → w = 3

Step 3: Check: P = 2(7 + 3) = 20 ✓

Advanced Example: Rectangle with Variables

Rectangle with P = 24, length = width + 2. Find both sides.

Step 1: Let width = x, length = x + 2

Step 2: P = 2(l + w) → 24 = 2((x + 2) + x) → 24 = 2(2x + 2)

Step 3: 24 = 4x + 4 → 20 = 4x → x = 5

Step 4: Width = 5, Length = 7. Check: P = 2(5 + 7) = 24 ✓

Memory Tip 1: "Perimeter" starts with "P" like "Perimeter is Plus" - you add all sides together.
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.
Worksheet Answer Key
P = sum of all sides
Universal Perimeter Formula
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

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

• General rule: P = sum of all side lengths

• Algebra rule: Use inverse operations to solve for unknowns

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.