Polygon: A closed shape made up of straight line segments
Perimeter: The total distance around the outside of a shape
- Identify all the sides of the polygon
- Add the lengths of all the sides together
- The sum is the perimeter of the polygon
Side 1 = 8 cm, Side 2 = 10 cm, Side 3 = 13 cm
Perimeter = 8 + 10 + 13 = 31 cm
The perimeter of the triangle is 31 cm
The perimeter of the triangle is 31 cm.
• Perimeter of polygon: Sum of all side lengths
• Triangle: 3-sided polygon
• Units: Linear units (cm, m, ft, etc.)
Rectangle: A 4-sided polygon with opposite sides equal
Perimeter of rectangle: P = 2(length + width)
Length = 12 cm, Width = 7 cm
Perimeter = 2(length + width) = 2(12 + 7) = 2(19) = 38 cm
The perimeter of the rectangle is 38 cm
The perimeter of the rectangle is 38 cm.
• Perimeter of rectangle: P = 2(l + w)
• Rectangle properties: Opposite sides are equal
• Units: Linear units (cm, m, ft, etc.)
Square: A 4-sided polygon with all sides equal
Perimeter of square: P = 4 × side length
Side = 9 inches
Perimeter = 4 × side = 4 × 9 = 36 inches
The perimeter of the square is 36 inches
The perimeter of the square is 36 inches.
• Perimeter of square: P = 4s
• Square properties: All sides are equal
• Units: Linear units (in, cm, ft, etc.)
Pentagon: A 5-sided polygon
Perimeter of polygon: Sum of all side lengths
Side 1 = 7 cm, Side 2 = 8 cm, Side 3 = 9 cm, Side 4 = 10 cm, Side 5 = 11 cm
Perimeter = 7 + 8 + 9 + 10 + 11 = 45 cm
The perimeter of the pentagon is 45 cm
The perimeter of the pentagon is 45 cm.
• Perimeter of polygon: Sum of all side lengths
• Pentagon: 5-sided polygon
• Units: Linear units (cm, m, ft, etc.)
Hexagon: A 6-sided polygon
Perimeter of polygon: Sum of all side lengths
Side 1 = 6 in, Side 2 = 7 in, Side 3 = 8 in, Side 4 = 7 in, Side 5 = 6 in, Side 6 = 9 in
Perimeter = 6 + 7 + 8 + 7 + 6 + 9 = 43 inches
The perimeter of the hexagon is 43 inches
The perimeter of the hexagon is 43 inches.
• Perimeter of polygon: Sum of all side lengths
• Hexagon: 6-sided polygon
• Units: Linear units (in, cm, ft, etc.)
Polygon: A closed shape made up of straight line segments
Perimeter: The total distance around the outside of a shape
Regular polygon: A polygon with all sides and angles equal
- Identify the polygon: Count the number of sides
- Measure all sides: Find the length of each side
- Add all side lengths: Sum them together
- State the answer: Include correct units
• Perimeter of any polygon: Sum of all side lengths
• Rectangle: P = 2(length + width)
• Square: P = 4 × side
• Regular polygon: P = number of sides × one side length
• Always include correct units in answers
Polygon: A closed shape made up of straight line segments (sides).
Perimeter: The total distance around the outside of a shape, measured in linear units.
Regular Polygon: A polygon with all sides and angles equal.
Irregular Polygon: A polygon with sides and/or angles of different measures.
Universal Rule: Perimeter = Sum of all side lengths.
Unit Consistency: Perimeter is always measured in linear units.
Counting Sides: Ensure you include every side in your calculation.
Measurement Accuracy: Precise measurements lead to accurate perimeters.
Step 1: Identify the polygon and count the number of sides.
Step 2: Measure or identify the length of each side.
Step 3: Add all the side lengths together.
Step 4: Express the answer with correct units.
Step 5: Verify your calculation for accuracy.
Triangle: Sides 8, 10, 13 cm → Perimeter = 8 + 10 + 13 = 31 cm.
Rectangle: Length 12 cm, Width 7 cm → Perimeter = 2(12 + 7) = 38 cm.
Square: Side 9 in → Perimeter = 4 × 9 = 36 in.
Pentagon: Sides 7, 8, 9, 10, 11 cm → Perimeter = 45 cm.
Tip 1: Draw and label the polygon to keep track of sides.
Tip 2: For regular polygons, multiply one side by the number of sides.
Tip 3: Always check that you haven't missed any sides.
Common Mistake: Adding the wrong number of sides.
Common Mistake: Forgetting to include units in the answer.
Memory Phrase: "Perimeter is the distance around the outside!"
Visual Cue: Imagine walking around the edge of the shape.
Formula Reminder: Add all sides together.
Always Remember: Perimeter uses linear units (cm, m, ft, etc.).
Success Strategy: Practice with different polygon shapes and sizes.
Questions & Answers
Question: How do I find the perimeter of a polygon if some sides are missing?
Answer: If some sides are missing, you'll need to use the properties of the polygon to find them:
- For rectangles: opposite sides are equal
- For squares: all sides are equal
- For regular polygons: all sides are equal
- For irregular polygons: you may need additional information
If you can't determine the missing side lengths, you cannot calculate the full perimeter.
Question: My child gets confused when working with different polygon names. How can I help them remember?
Answer: Here are strategies to remember polygon names:
- Triangle: 3 sides (think "tri-" = three)
- Quadrilateral: 4 sides ("quad-" = four)
- Pentagon: 5 sides ("pent-" = five)
- Hexagon: 6 sides ("hex-" = six)
- Octagon: 8 sides ("oct-" = eight)
Practice drawing different polygons and labeling them. The more they see and use the names, the more familiar they'll become.
Question: Does the order matter when I add the sides to find perimeter?
Answer: No, the order doesn't matter when adding the sides because addition is commutative. This means that changing the order of numbers being added doesn't change the sum. For example:
Triangle with sides 8, 10, and 13: 8 + 10 + 13 = 31
Same triangle: 13 + 8 + 10 = 31
However, it's helpful to add in order to avoid missing any sides. You can group numbers that are easier to add together first (like 8 + 2 = 10).