The perimeter is the distance around the outside of a two-dimensional shape. This distance is the length of the shape’s boundary. We measure the perimeter in linear units, such as centimeters, inches, or meters. The perimeter is really useful for everyday tasks. For example, when we need to put up a fence around a yard, the yard’s perimeter is important. It is also important when we frame a picture or wrap a gift. The perimeter is the distance around the outside of the shape, like the yard, the picture or the 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 a 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 a 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

4. Perimeter of Irregular Polygons

Method: Add all side lengths.

Example (Pentagon):

Sides: 5, 6, 5, 6, 5 units

Perimeter=5+6+5+6+5=27 units

Perimeter=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

1. Pentagon Example:

* Sides: 5 units, 6 units, 5 units, 6 units, 5 units

* Perimeter = 5+6+5+6+5=27 units

1. Hexagon Example:

* Sides: 4 units each

* Perimeter = 4+4+4+4+4+4=24 units

* Alternatively: Perimeter = 6×4=24 units

Exercises

Exercise 1. Let us do an exercise. We have to find the perimeter of rectangles. To do this we need to know what a rectangle is. A rectangle is a shape with four sides. The perimeter of rectangles is the distance around the outside of the rectangles. We can find the perimeter of rectangles by adding up the lengths of all the sides of the rectangles.

We can use a formula to find the perimeter of rectangles. The formula is this: perimeter of rectangles equals two times the length of the rectangles plus two times the width of the rectangles.

Now we can try to find the perimeter of rectangles using this formula. We just need to know the length and width of the rectangles. Then we can plug these numbers into the formula. Calculate the perimeter of rectangles.

For example let us say we have a rectangle with a length of five units and a width of three units. We can use the formula to find the perimeter of this rectangle. The perimeter of the rectangle equals two times the length of the rectangle plus two times the width of the rectangle.

So the perimeter of the rectangle equals two times five units plus two times three units. This is equal, to ten units plus six units. Therefore the perimeter of the rectangle equals sixteen units.

We can do this with any rectangle. We just need to know the length and width of the rectangles. Then we can find the perimeter of the 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. To find the perimeter of a square, we need to know that a square has four sides. The perimeter of a square is the distance, around the square. We calculate the perimeter of squares by adding up the lengths of all four sides. Since all the sides of a square are equal, we can find the perimeter of a square by multiplying the length of one side by four. This is a way to find the perimeter of squares. When we multiply the length of one side of a square by 4, we get the square’s perimeter.

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

We need to determine whether the statements are true or false.

1. So I have this rectangle. It is 4 units long and 3 units wide. The perimeter of this rectangle is the distance around it. To find the perimeter of the rectangle, you need to add up all the sides. The rectangle has two sides that are 4 units long and two sides that are 3 units wide. If you add these sides together, you get 4 units + 4 units. 3 Units + 3 units. This equals 14 units. So the perimeter of the rectangle is really 14 units.

2. So we have a square and the length of each side of this square is 5 units. The perimeter of this square is the distance around the square, which is 20 units.

3. The perimeter of a rectangle with length 7 units and width 2 units is 18 units.

4. So we have a square and the length of each side of this square is 6 units. The perimeter of this square is the distance around the square. To find the perimeter of the square we add up all the sides of the square. Since all the sides of the square are equal, the perimeter of the square is 6 units plus 6 units plus 6 units plus 6 units, which is 24 units. This means the perimeter of the square is 24 units.

5. So the rectangle has a length of 8 units and a width of 4 units. The perimeter of a rectangle is the distance around it. To find the perimeter of the rectangle, we add up all the sides of the rectangle. The perimeter of this rectangle is 24 units because that is the distance, around the rectangle. The rectangle has a perimeter of 24 units.

Let us do Exercise 4. We have to find the perimeter of each polygon. The perimeter of a polygon is the distance around the outside of the polygon. To find the perimeter of each polygon we need to add up the lengths of all the sides of the polygon. We will do this for each polygon.

We will look at each polygon. Find the perimeter. The perimeter is the length of the sides of the polygon. We will calculate this for each polygon.

* We will start with the polygon

* Then we will do the polygon

* We will keep doing this for each polygon

The perimeter of each polygon is important. We need to 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

We need to figure out 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. So we have a quadrilateral and all of its sides are the same each side is 4 units. This quadrilateral has four sides that’re all 4 units. If we add up all the sides of this quadrilateral which’re 4 units, 4 units, 4 units and 4 units the total is 16 units. The perimeter of this quadrilateral is 16 units, since it has four sides measuring 4 units each.

3. The perimeter of a pentagon with sides 2 units each is 12 units.

4. So we have a hexagon and each of its sides is 6 units long. The perimeter of this hexagon is 36 units. This makes sense because a hexagon has 6 sides and when we add up all the sides of this hexagon we get 36 units. The hexagon is a shape with 6 sides, and the perimeter of the hexagon is the length of all its sides.

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