Solved Exercises on Perimeter of Polygons in Grade 3

Master perimeter calculations: triangles, rectangles, squares, and other polygons through these 5 detailed exercises with step-by-step solutions.

Solution: Exercises 1 to 3
1 Finding perimeter of a rectangle
Exercise 1
A rectangle has a length of 8 cm and a width of 5 cm. Find the perimeter of the rectangle.
Definition:

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

Perimeter calculation method:
  1. Identify the length and width of the rectangle
  2. Add the length and width together
  3. Multiply the sum by 2
  4. Include the unit of measurement in your answer
Given
Length = 8 cm, Width = 5 cm
Formula
P = 2(l + w)
Result
P = 26 cm
Step 1: Identify the dimensions

Length = 8 cm, Width = 5 cm

Step 2: Apply the formula

Perimeter = 2 × (length + width)

Perimeter = 2 × (8 + 5)

Step 3: Calculate inside parentheses

8 + 5 = 13

Step 4: Multiply by 2

2 × 13 = 26

Final answer:

The perimeter of the rectangle is 26 centimeters.

Applied rules:

• Rectangle perimeter: P = 2(l + w)

• Order of operations: Parentheses first, then multiplication

• Units: Always include the unit of measurement

2 Finding perimeter of a triangle
Exercise 2
A triangle has sides measuring 6 cm, 8 cm, and 10 cm. Find the perimeter of the triangle.
Definition:

Triangle perimeter: The sum of all three sides. P = side1 + side2 + side3.

Step 1: Identify all side lengths

Side 1 = 6 cm, Side 2 = 8 cm, Side 3 = 10 cm

Step 2: Apply the formula

Perimeter = Side 1 + Side 2 + Side 3

Perimeter = 6 + 8 + 10

Step 3: Add the measurements

6 + 8 = 14, then 14 + 10 = 24

Step 4: Include the unit

Perimeter = 24 cm

Final answer:

The perimeter of the triangle is 24 centimeters.

Applied rules:

• Triangle perimeter: Sum of all three sides

• Addition: Combine all side lengths

• Units: Always include the unit of measurement

3 Finding perimeter of a square
Exercise 3
A square has sides that are each 7 cm long. Find the perimeter of the square.
Definition:

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

Step 1: Identify the side length

All sides = 7 cm

Step 2: Apply the formula

Perimeter = 4 × side length

Perimeter = 4 × 7

Step 3: Multiply

4 × 7 = 28

Step 4: Include the unit

Perimeter = 28 cm

Final answer:

The perimeter of the square is 28 centimeters.

Applied rules:

• Square perimeter: P = 4s (where s is side length)

• Multiplication: 4 times the side length

• Units: Always include the unit of measurement

Key Concepts: Perimeter Calculations
P = 2(l + w)
Rectangle Perimeter
P = 4s
Square Perimeter
P = \text{side}_1 + \text{side}_2 + \text{side}_3 + ...
Polygon Perimeter
Rectangle
P = 2(l + w)
2 pairs of equal sides
Square
P = 4s
4 equal sides
Triangle
P = a + b + c
Sum of 3 sides
Regular Polygon
P = n × s
n sides of length s
Irregular Polygon
P = sum of sides
Add all side lengths
Perimeter
Distance Around
Boundary length
Key definitions:

Perimeter: The total distance around the outside edge of a two-dimensional shape.

Rectangle: A four-sided shape with four right angles and opposite sides equal.

Square: A four-sided shape with four equal sides and four right angles.

Triangle: A three-sided polygon with three angles.

Side length: The measurement of one edge of a polygon.

Regular polygon: A polygon with all sides and angles equal.

Irregular polygon: A polygon with sides and angles that are not all equal.

Complete perimeter calculation methodology:
  1. Identify the shape: Determine what type of polygon you're working with
  2. Measure sides: Find the length of each side (or use given measurements)
  3. Select formula: Choose the appropriate perimeter formula for the shape
  4. Substitute values: Replace variables in the formula with actual measurements
  5. Calculate: Perform the arithmetic operations
  6. Check units: Ensure all measurements are in the same unit
  7. State answer: Include the unit of measurement in your final answer
Tip 1: To remember perimeter, think "perimeter" sounds like "around" - it's the distance around the shape.
Tip 2: For rectangles, you can add length + width + length + width, or use the formula 2(length + width).
Tip 3: Always double-check that you've added ALL sides when calculating perimeter.
Tip 4: Draw a picture and label the sides to visualize the problem better.
Common mistakes: Forgetting to add all sides, mixing up units of measurement, confusing perimeter with area.
Real-world applications: Fencing a garden, putting trim around a room, framing a picture.
Essential perimeter rules:

• Perimeter is the sum of all side lengths

• All measurements must be in the same unit

• Rectangle: P = 2(length + width)

• Square: P = 4 × side length

• Triangle: P = sum of all three sides

• Always include units in your final answer

Solution: Exercises 4 to 5
4 Finding perimeter of an irregular polygon
Exercise 4
A pentagon has sides measuring 4 cm, 6 cm, 5 cm, 7 cm, and 3 cm. Find the perimeter of the pentagon.
Definition:

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

Step 1: List all side lengths

Sides: 4 cm, 6 cm, 5 cm, 7 cm, 3 cm

Step 2: Apply the formula

Perimeter = sum of all sides

Perimeter = 4 + 6 + 5 + 7 + 3

Step 3: Add the measurements

4 + 6 = 10, 10 + 5 = 15, 15 + 7 = 22, 22 + 3 = 25

Step 4: Include the unit

Perimeter = 25 cm

Final answer:

The perimeter of the pentagon is 25 centimeters.

Applied rules:

• Irregular polygon perimeter: Sum of all side lengths

• Addition: Combine all measurements

• Units: Always include the unit of measurement

5 Word problem with perimeter
Exercise 5
Sarah wants to put a fence around her rectangular garden that is 12 meters long and 8 meters wide. How many meters of fencing does she need?
Definition:

Word problems: Real-life situations that require mathematical calculations to solve.

Step 1: Identify the problem

Sarah needs fencing for the perimeter of her rectangular garden

Step 2: Identify the dimensions

Length = 12 m, Width = 8 m

Step 3: Apply the rectangle perimeter formula

Perimeter = 2(length + width)

Perimeter = 2(12 + 8)

Step 4: Calculate

12 + 8 = 20, then 2 × 20 = 40

Step 5: State the answer

Sarah needs 40 meters of fencing

Final answer:

Sarah needs 40 meters of fencing to surround her garden.

Applied rules:

• Real-world application: Perimeter = fencing needed

• Rectangle formula: P = 2(l + w)

• Units: Always include the unit of measurement

Complete Guide: Perimeter of Polygons
P_{\text{rectangle}} = 2(l + w)
Rectangle Formula
P_{\text{square}} = 4s
Square Formula
Key definitions:

Perimeter: The total distance around the boundary of a two-dimensional shape. It's a linear measurement.

Linear measurement: Measurement of distance, typically in units like centimeters, meters, inches, or feet.

Polygon: A closed shape made up of straight line segments.

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

Irregular polygon: A polygon where sides and/or angles are not all equal.

Complete problem-solving methodology:
  1. Read carefully: Understand what is being asked
  2. Identify the shape: Determine what type of polygon is involved
  3. Gather information: Note all given side lengths or dimensions
  4. Choose the method: Select the appropriate perimeter formula
  5. Substitute values: Put the known measurements into the formula
  6. Calculate: Perform the mathematical operations
  7. Check work: Verify that all sides were included and calculations are correct
  8. State answer: Provide the final answer with correct units
Tip 1: Remember that perimeter is always a linear measurement (distance around).
Tip 2: For squares, you only need to know one side length to calculate the perimeter.
Tip 3: When working with rectangles, opposite sides are always equal in length.
Tip 4: Draw and label shapes to visualize the problem and avoid missing any sides.
Common applications: Fencing, border trim, frame measurements, running tracks, walking paths.
Unit consistency: All measurements must be in the same unit before calculating perimeter.
Essential perimeter rules:

• General rule: Perimeter = sum of all side lengths

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

• Square: P = 4 × side length = 4s

• Triangle: P = side₁ + side₂ + side₃

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

• Irregular polygon: P = sum of all different side lengths

• Units: Always include the unit of measurement in your answer

Questions & Answers

Question: Why do we multiply by 2 when finding the perimeter of a rectangle? Shouldn't we add all 4 sides?

Answer: Actually, both methods work! When we use P = 2(l + w), we ARE adding all 4 sides:

  • A rectangle has 2 lengths and 2 widths
  • So we could write: P = l + w + l + w
  • This simplifies to: P = 2l + 2w
  • Factoring out the 2: P = 2(l + w)

So P = 2(l + w) is just a shorter way of saying "add all 4 sides" because opposite sides of a rectangle are equal!

Question: What's the difference between perimeter and area? They both deal with shapes, right?

Answer: Perimeter and area are different measurements:

  • Perimeter: Measures the distance around the outside of a shape (like walking around a garden)
  • Area: Measures the space inside a shape (like covering a floor with tiles)
  • Perimeter is measured in linear units (cm, m, ft)
  • Area is measured in square units (cm², m², ft²)

Think of perimeter as the fence around your yard and area as the grass inside the fence.

Question: Do I always have to measure every side of a shape to find the perimeter?

Answer: Not always! It depends on the shape:

  • Square: Measure one side and multiply by 4 (all sides equal)
  • Rectangle: Measure length and width, then use P = 2(l + w) (opposite sides equal)
  • Regular polygon: Measure one side and multiply by the number of sides
  • Irregular polygon: You must measure each side individually and add them all

If a shape has equal sides or pairs of equal sides, you can use shortcuts!