When we start learning about Year 7 Mathematics, we often come across the words "perimeter" and "circumference."

They might sound similar, but they mean different things. Knowing these differences is really important for understanding measurements.

What is Perimeter?

The perimeter is the total distance around a shape with straight sides, which we call a polygon.

Imagine you are walking around a shape. The distance you walk is the perimeter.

To find the perimeter, you can use different formulas based on the shape:

• Rectangle: For a rectangle that is 4 cm long and 3 cm wide, you can find the perimeter with this formula:

$$\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (4 + 3) = 2 \times 7 = 14 \text{ cm}$$

• Square: For a square, which has all four sides the same length, if each side is 5 cm long, the perimeter is:

$$\text{Perimeter} = 4 \times \text{Side} = 4 \times 5 = 20 \text{ cm}$$

• Triangle: For a triangle with sides that are 3 cm, 4 cm, and 5 cm, you get the perimeter by adding all the sides:

$$\text{Perimeter} = 3 + 4 + 5 = 12 \text{ cm}$$

What is Circumference?

Now, circumference is a special term for the distance around a circle.

While it is a type of perimeter, it only applies to circles.

You can find the circumference using either the radius (the distance from the center to the edge) or the diameter (the distance across the circle through the center).

1. Using Radius: The formula for finding the circumference with the radius ($r$) is:

$$\text{Circumference} = 2 \pi r$$

For example, if the radius of a circle is 3 cm:

$$\text{Circumference} = 2 \times \pi \times 3 \approx 18.84 \text{ cm} \quad (\text{using } \pi \approx 3.14)$$

2. Using Diameter: If you know the diameter ($d$), the formula is:

$$\text{Circumference} = \pi d$$

So if the diameter is 6 cm:

$$\text{Circumference} = \pi \times 6 \approx 18.84 \text{ cm}$$

In Summary

• Perimeter is for shapes with straight sides like rectangles, squares, and triangles. It measures the total length around these shapes.

• Circumference is specifically for circles.

Knowing these terms will make it easier for you to solve measurement problems in math.

Happy calculating!