Complete Perimeter and Area of Polygons Worksheet for 3rd Grade

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

Perimeter Worksheet Solutions
1 Rectangle perimeter
Exercise 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
Exercise 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
Exercise 3
A triangle has sides of 5 cm, 6 cm, and 7 cm. What is its perimeter?
Definition:

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

Given
a = 5, b = 6, c = 7
Formula
P = a + b + c
Calculate
P = 18 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 = 5 + 6 + 7

Step 3: Calculate

P = 18

Step 4: Include unit

The perimeter is 18 cm.

Perimeter = 18 cm
Final answer:

The perimeter of the triangle is 18 cm.

Applied rules:

• Triangle perimeter formula: Sum of all three sides

• Addition: Add all three side lengths

• Verification: Check that you added all sides

Area Worksheet Solutions
Problem Set A
Problem A1: A rectangle has a length of 9 cm and a width of 4 cm. What is its area?
Problem A2: A square has sides of 6 cm. What is its area?
Problem A3: A rectangle has a length of 12 cm and a width of 5 cm. What is its area?
Problem Set B
Problem B1: A square has sides of 10 cm. What is its area?
Problem B2: A rectangle has a length of 7 cm and a width of 8 cm. What is its area?
Problem B3: A square has sides of 3 cm. What is its area?
▭
Rectangle

P = 2(l+w)

A = l×w

□
Square

P = 4s

A = s²

△
Triangle

P = a+b+c

A = ½bh

⬟
Polygon

P = sum of sides

Varies

Area: A = length × width
Area of Rectangle
Rectangle
P = 2(l + w)
Perimeter
Rectangle
A = l × w
Area
Square
P = 4s
Perimeter
Square
A = s²
Area
Problem-Solving Steps:
  1. Identify the shape and its properties
  2. Determine what to calculate (perimeter or area)
  3. Select the correct formula for the shape
  4. Substitute values into the formula
  5. Calculate the result
  6. Include the correct unit in your answer
Polygon Worksheet Exercises
4 Pentagon perimeter
Exercise 4
A pentagon has sides of 4 cm, 5 cm, 6 cm, 7 cm, and 8 cm. What is its perimeter?
Definition:

Polygon Perimeter: Sum of all sides. For any polygon: P = sum of all side lengths.

Given
sides = 4,5,6,7,8
Formula
P = sum of sides
Calculate
P = 30 cm
Step 1: Write the perimeter formula for a polygon

For any polygon: Perimeter = sum of all side lengths

Step 2: Add all side lengths

P = 4 + 5 + 6 + 7 + 8

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

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

Given
side = 5 cm
Formula
P = 6s
Calculate
P = 30 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(5)

Step 3: Calculate

P = 30

Step 4: Include unit

The perimeter is 30 cm.

Perimeter = 30 cm
Final answer:

The perimeter of the hexagon is 30 cm.

Complete Summary: Perimeter and Area of 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.

Area: The amount of space inside a 2D shape. It's like covering the entire surface with squares.

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.

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

• Rectangle Area: A = length × width

• Square Area: A = side²

Step-by-Step Method for Perimeter:
  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.)
Step-by-Step Method for Area:
  1. Identify the shape: Determine if it's a rectangle, square, etc.
  2. Select the formula: Use the correct area formula
  3. Substitute values: Put the measurements into the formula
  4. Calculate: Do the multiplication
  5. State the answer: Include the unit (cm², m², 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

Area Example: Rectangle

Rectangle with length = 8 cm and width = 5 cm

Step 1: A = l × w = 8 × 5 = 40 cm²

Step 2: The area is 40 cm²

Perimeter Example: Square

Square with side = 6 cm

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

Step 2: The perimeter is 24 cm

Area Example: Square

Square with side = 6 cm

Step 1: A = s² = 6² = 36 cm²

Step 2: The area is 36 cm²

Memory Tip 1: "Perimeter" sounds like "fence-meter" - you measure the fence around a yard!
Memory Tip 2: "Area" sounds like "are-a" - it covers the whole area inside!
Memory Tip 3: Perimeter = outside edge, Area = inside space.
Common Mistake: Don't confuse perimeter (addition) with area (multiplication).
Common Mistake: Always include units in your answer (cm, m, cm², m², etc.)
Key Takeaways: 1) Perimeter measures the outside edge, 2) Area measures the inside space, 3) Use different formulas for each.
Real World Application: Perimeter for fencing, area for carpeting or painting.
Worksheet Answer Key
P = sum of all sides
Perimeter Formula
A = length × width
Area Formula
Perimeter Formulas:

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

Polygon: P = sum of all side lengths

Area Formulas:

Rectangle: A = l × w where l = length, w = width

Square: A = s² where 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 or area formula
  3. Substitute known values: Fill in the given measurements
  4. Calculate: Perform the necessary arithmetic operations
  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/area with your solution.
Common errors: Forgetting that rectangles have 2 lengths and 2 widths, mixing up perimeter and area formulas, arithmetic mistakes.
Key formulas: Rectangle: P=2(l+w), A=l×w, Square: P=4s, A=s²
Essential rules to remember:

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

• Square rule: P = 4 × side length, A = side²

• Triangle rule: P = side₁ + side₂ + side₃

• General rule: P = sum of all side lengths

• Units: Perimeter in cm, m, inches; Area in cm², m², etc.

Examples: P=2(5+3)=16, A=5×3=15, P=4(5)=20, A=5²=25
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 the difference between perimeter and area. How can I help them understand?

Answer: Here's a helpful way to explain the difference:

  1. Perimeter: Think of it as building a fence around a yard - you measure the distance around the outside
  2. Area: Think of it as covering the floor with tiles - you measure the space inside

Use physical examples: If you have a rectangular piece of paper:

  • Perimeter = measure the tape needed to go around the edge
  • Area = count how many small squares fit inside

Perimeter is measured in units (cm, m), while area is measured in square units (cm², m²).

Question: Are there any memory tricks to remember the different perimeter and area formulas?

Answer: Yes! Here are some effective memory tricks:

  • Perimeter: "Perimeter = Peri-Meter (around-measure)" - it goes around the shape
  • Area: "Area = Are-A (the space inside)"
  • Rectangle Perimeter: "Two lengths, two widths" → P = 2(l + w)
  • Square Perimeter: "Four equal sides" → P = 4s
  • Rectangle Area: "Length times width" → A = l × w
  • Square Area: "Side times side" → A = s²

Physical activity: Walk around the perimeter of different shaped objects while counting the sides out loud, and trace the area with your hand to cover the space inside.