Perimeter is the total distance around the outside of a two-dimensional shape. It represents the length of the shape’s boundary and is measured in linear units (like centimeters, inches, or meters). Perimeter helps in real-world tasks like fencing a yard, framing a picture, or wrapping a gift.

How to Calculate Perimeter

1. Perimeter of a Rectangle

Formula:Perimeter=2×(Length+Width)Perimeter=2×(Length+Width)

Why? A rectangle has two pairs of equal sides.

Example:
A rectangle has a length of 5 units and width of 3 units.

Perimeter=2×(5+3)=16 units

Perimeter=2×(5+3)=16 units

2. Perimeter of a Square

Formula:Perimeter=4×SidePerimeter=4×Side

Why? All four sides are equal.

Example:
A square has side length = 4 units.

Perimeter=4×4=16 units

Perimeter=4×4=16 units

3. Perimeter of a Triangle

Formula:Perimeter=Side1+Side2+Side3Perimeter=Side1​+Side2​+Side3​

Example:
A triangle has sides 3, 4, and 5 units.

Perimeter=3+4+5=12 units

Perimeter=3+4+5=12 units

4. Perimeter of Irregular Polygons

Method: Add all side lengths.

Example (Pentagon):
Sides: 5, 6, 5, 6, 5 unitsPerimeter=5+6+5+6+5=27 unitsPerimeter=5+6+5+6+5=27 units

Example (Hexagon with equal sides):
Each side = 4 units

Perimeter=6×4=24 units

Perimeter=6×4=24 units

Examples:

1. Rectangle Example:
   • Length = 5 units, Width = 3 units
   • Perimeter = 2×(5+3)=2×8=16 units
2. Square Example:
   • Side = 4 units
   • Perimeter = 4×4=16 units
3. Triangle Example:

• Sides: 3 units, 4 units, 5 units
• Perimeter = 3+4+5=12 units

4. Pentagon Example:

• Sides: 5 units, 6 units, 5 units, 6 units, 5 units
• Perimeter = 5+6+5+6+5=27 units

5. Hexagon Example:

• Sides: 4 units each
• Perimeter = 4+4+4+4+4+4=24 units
• Alternatively: Perimeter = 6×4=24 units

Exercises

Exercise 1: Find the Perimeter of Rectangles

Use the formula Perimeter=2×(Length+Width)\text{Perimeter} = 2 \times (\text{Length} + \text{Width})Perimeter=2×(Length+Width) to find the perimeter of each rectangle:

1. Length = 7 units, Width = 4 units
2. Length = 9 units, Width = 5 units
3. Length = 6 units, Width = 2 units
4. Length = 8 units, Width = 3 units
5. Length = 5 units, Width = 5 units

Exercise 2: Find the Perimeter of Squares

Use the formula Perimeter=4×Side\text{Perimeter} = 4 \times \text{Side}Perimeter=4×Side to find the perimeter of each square:

1. Side = 6 units
2. Side = 5 units
3. Side = 7 units
4. Side = 3 units
5. Side = 8 units

Exercise 3: True or False

Decide if the statements are true or false:

1. The perimeter of a rectangle with length 4 units and width 3 units is 14 units.
2. A square with side length 5 units has a perimeter of 20 units.
3. The perimeter of a rectangle with length 7 units and width 2 units is 18 units.
4. A square with side length 6 units has a perimeter of 24 units.
5. The perimeter of a rectangle with length 8 units and width 4 units is 24 units.

Exercise 4: Find the Perimeter of Each Polygon

Add the lengths of the sides to find the perimeter:

1. Triangle with sides 4 units, 6 units, and 7 units
2. Quadrilateral with sides 5 units, 5 units, 7 units, and 8 units
3. Pentagon with sides 3 units, 3 units, 4 units, 4 units, and 5 units
4. Hexagon with all sides measuring 3 units

Exercise 5: True or False

Determine if the statements are true or false:

1. The perimeter of a triangle with sides 5 units, 5 units, and 5 units is 15 units.
2. A quadrilateral with sides 4 units, 4 units, 4 units, and 4 units has a perimeter of 16 units.
3. The perimeter of a pentagon with sides 2 units each is 12 units.
4. A hexagon with sides of 6 units each has a perimeter of 36 units.
5. The perimeter of a triangle with sides 8 units, 2 units, and 2 units is 10 units.

Perimeter vs. Area: Key Differences

Feature	Perimeter	Area
Measures	Boundary length	Surface coverage
Units	Linear (cm, m)	Square (cm², m²)
Formula (Rectangle)	2×(L+W)2×(L+W)	L×WL×W

📌 Remember: Perimeter is the fence around a shape, while area is the grass inside.

Mastering perimeter calculations helps in practical tasks and STEM fields. Key takeaways:

1. Rectangles: Use 2×(L+W)2×(L+W)
2. Squares: Use 4×Side4×Side
3. Irregular shapes: Sum all side lengths