Perimeter (Grade 12 NSC Matric Mathematical Literacy): Revision Notes

Perimeter

What is perimeter?

Perimeter is the total distance around the outside edge of a shape. Think of it as the length of the boundary that encloses a closed geometric figure. When you walk around the edge of a garden, sports field, or any enclosed area, you are following the perimeter.

Perimeter is measured in units of length such as millimetres (mm), centimetres (cm), metres (m), or kilometres (km).

Basic perimeter formulas

The method for calculating perimeter depends on the shape you are working with. Different shapes require different approaches, but the underlying concept remains the same - you're finding the total distance around the outside edge.

Rectangle

For a rectangle with length $l$ and width $w$: Perimeter = $2 \times \text{length} + 2 \times \text{width}$

This works because a rectangle has two pairs of equal sides.

Square

For a square with side length $s$: Perimeter = $4 \times \text{side length}$

Since all four sides of a square are equal, you multiply the side length by 4.

Triangle

For any triangle with sides of length $a$, $b$, and $c$: Perimeter = $\text{side } a + \text{side } b + \text{side } c$

Simply add up the lengths of all three sides.

Circle (Circumference)

For a circle with radius $r$: Circumference = $\pi \times (2 \times \text{radius})$ or $\pi \times \text{diameter}$

Remember that circumference is the special name for the perimeter of a circle. Use $\pi = 3.142$ for calculations unless told otherwise.

How to measure perimeter

There are two main approaches to finding perimeter, each suited to different situations:

Direct measurement method

For rectangles, squares, and triangles, you can measure each side using a ruler and add the lengths together. This method is practical when you have the actual object in front of you.

Using formulas

When you know the dimensions of a shape, using the appropriate formula is more efficient and accurate than direct measurement. This method is essential when working with scale drawings or when precise calculations are needed.

Scale drawings and perimeter

Scale drawings represent real objects at a reduced size. Understanding how to work with scales is crucial for real-world applications.

When working with scale drawings, follow this systematic approach:

1. First measure the perimeter on the drawing
2. Then multiply by the scale factor to find the actual perimeter
3. Convert units if necessary

Worked examples

The following examples demonstrate how to apply perimeter formulas in practical situations:

Key exam tips

Success in perimeter questions requires attention to detail and systematic working. Here are essential strategies to help you achieve the best results:

• Always check units: Make sure your answer is in the correct units (mm, cm, m, km)
• Show your working: Write down the formula first, then substitute values
• Scale conversions: Remember to multiply diagram measurements by the scale factor
• Circle terminology: Circumference is the perimeter of a circle
• Rounding: Follow instructions for decimal places or significant figures
• Formula accuracy: You will be given perimeter formulas in exams, but knowing them helps with speed