Complete Guide to Finding Perimeter Unknown Sides for 3rd Grade

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

Solution: Exercises 1 to 3
1 Rectangle with unknown side
Exercise 1
A rectangle has a perimeter of 20 cm. One side measures 6 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 = 20, one side = 6
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

20 = 2(6 + w)

Step 3: Solve for the unknown

Divide both sides by 2: 10 = 6 + w

Subtract 6 from both sides: 10 - 6 = w

w = 4

Step 4: Verify the answer

P = 2(6 + 4) = 2(10) = 20 ✓

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 24 cm. What is the length of each side?
Definition:

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

Given
P = 24
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

24 = 4s

Step 3: Solve for the side length

Divide both sides by 4: s = 24 ÷ 4

s = 6

Step 4: Verify the answer

P = 4(6) = 24 ✓

Each side is 6 cm
Final answer:

Each side of the square is 6 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 18 cm. Two sides measure 5 cm and 7 cm. What is the length of the third side?
Definition:

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

Given
P = 18, a = 5, b = 7
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

18 = 5 + 7 + c

Step 3: Simplify and solve for the unknown

18 = 12 + c

c = 18 - 12

c = 6

Step 4: Verify the answer

P = 5 + 7 + 6 = 18 ✓

The third side is 6 cm
Final answer:

The length of the third side is 6 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

Perimeter Formulas & Methods
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
▭
Rectangle
P = 2(l + w)

Length and width are different

□
Square
P = 4s

All sides equal

△
Triangle
P = a + b + c

Three sides

⬟
Polygon
P = sum of sides

Add all sides

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 Exercises & Practice
4 Irregular polygon
Exercise 4
A pentagon has a perimeter of 30 cm. Four sides measure 5 cm, 6 cm, 4 cm, and 7 cm. Find the fifth side.
Definition:

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

Given
P = 30, sides = 5,6,4,7
Formula
P = s₁+s₂+s₃+s₄+s₅
Unknown
s₅ = ?
Step 1: Write the perimeter formula

For a pentagon: P = s₁ + s₂ + s₃ + s₄ + s₅

Step 2: Substitute known values

30 = 5 + 6 + 4 + 7 + s₅

Step 3: Simplify and solve

30 = 22 + s₅

s₅ = 30 - 22 = 8

Step 4: Verify

P = 5 + 6 + 4 + 7 + 8 = 30 ✓

Fifth side = 8 cm
Final answer:

The fifth side is 8 cm.

5 Rectangle with variables
Exercise 5
A rectangle has a perimeter of 28 cm. If one side is 3 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+3
Formula
P = 2(l+w)
Equation
28 = 2(x+x+3)
Step 1: Define variables

Let width = x, then length = x + 3

Step 2: Set up equation

28 = 2(x + (x + 3))

28 = 2(2x + 3)

Step 3: Solve

28 = 4x + 6

22 = 4x

x = 5.5

Step 4: Find both sides

Width = 5.5 cm, Length = 5.5 + 3 = 8.5 cm

Step 5: Verify

P = 2(5.5 + 8.5) = 2(14) = 28 ✓

Width = 5.5 cm, Length = 8.5 cm
Final answer:

The sides are 5.5 cm and 8.5 cm.

Perimeter Laws, Methods, Definitions & Expressions
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.