🔲 Rectangle perimeter: the (L + l) × 2 formula and worked examples

The perimeter of a rectangle is the length around its edge: the distance a little ant would travel if it walked all the way around the shape and ended up back where it started. It sounds simple, but children often get confused—mixing up the edge with the area, forgetting half the sides, or writing “cm²” instead of “cm”.

Good news: it all comes down to a short formula, (L + l) × 2, and a few habits to build. Here’s how you can explain it at home this evening, with clear examples, the right units, and three simple activities to help your child remember for good.

The perimeter is the distance around the shape

Before you mention any formula, help your child feel what perimeter means. Ask them to trace their finger around the edge of a book, a placemat, or the fridge door, starting and finishing at the same corner. That journey is the perimeter. We only care about the edge: what’s inside doesn’t matter.

In everyday life, you need the perimeter whenever you want to go around something: fencing a vegetable patch, stringing lights around a window, wrapping a ribbon around a flat present, or sticking a border around a noticeboard. A good test for your child: “Am I looking for the distance around, or what fills the space?” If the answer is “around”, it’s a perimeter.

A rectangle has a special feature that makes things easier: its opposite sides are the same length. So there are two long sides, called the lengths (L), and two short sides, the widths (l). All four corners are right angles.

The formula for the perimeter of a rectangle: (L + l) × 2

To go all the way around a rectangle, you walk along one length, one width, another length, and another width. So you can write the calculation in three ways, all giving the same answer:

• L + l + L + l: add up all four sides, one by one;
• (L + l) × 2: add one length and one width, then double it;
• 2 × L + 2 × l: double the length, double the width, then add them together.

Let’s take a vegetable patch that’s 6 m long and 4 m wide. First method: 6 + 4 + 6 + 4 = 20 m. Second: (6 + 4) × 2 = 10 × 2 = 20 m. Third: 2 × 6 + 2 × 4 = 12 + 8 = 20 m. Three ways, one answer: your child can use whichever makes most sense, as long as they know why it works.

Watch out for the brackets in the formula (L + l) × 2. They mean you add first. Without them, “6 + 4 × 2” is worked out as 6 + 8 = 14, which is wrong for our vegetable patch. If brackets are confusing, write the calculation in two lines: “6 + 4 = 10”, then “10 × 2 = 20”.

Worked examples, from notebook to garden

The best practice is to measure real objects at home. Here are some examples you can use as they are; each calculation has been checked.

The last line needs a note: a square is a special kind of rectangle, with all four sides equal. So you can use the rectangle formula, (5 + 5) × 2 = 20 cm, or the shortcut for a square, side × 4 = 20 cm.

Notice that every calculation comes down to two steps: an addition, then a double. Doubling 25, 50.7 or 37 in your head is just another skill to practise; we explain several strategies in our article on mental maths in CM1. A child who can double quickly will work out perimeters without needing to write it all down.

Units: the pitfall that loses marks

Perimeter is a length. So it’s written in the same unit as the sides: centimetres for a drawing in a notebook, metres for a room or garden, kilometres for the edge of a lake. Never “cm²” or “m²”: those square units are for measuring area, not the outline.

The second pitfall is mixing units. If a question gives a table that’s 1.60 m by 90 cm, you can’t just add 1.60 and 90. First, convert everything to the same unit:

• in centimetres: 1.60 m = 160 cm, then (160 + 90) × 2 = 250 × 2 = 500 cm;
• in metres: 90 cm = 0.90 m, then (1.60 + 0.90) × 2 = 2.50 × 2 = 5 m.

Both answers are correct, since 500 cm = 5 m. There are only a few conversions to remember: 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1,000 m.

Finding a missing side from the perimeter

In CM1 and CM2, the exercises are reversed: you’re given the perimeter and one side, and need to find the other. The key is the half-perimeter—that’s half the way round, which equals one length plus one width.

Example: a rectangle has a perimeter of 30 cm and a length of 9 cm. What is its width?

1. Half-perimeter: 30 ÷ 2 = 15 cm (that’s L + w).
2. Width: 15 − 9 = 6 cm.
3. Check: (9 + 6) × 2 = 15 × 2 = 30 cm. The calculation is correct.

For a square, it’s even simpler: a square with a perimeter of 36 cm has sides of 36 ÷ 4 = 9 cm. Always encourage the checking step: it only takes a few seconds and catches lots of little mistakes.

Perimeter or area: how not to mix them up

This is a very common mix-up in primary school. The perimeter measures the edge; the area measures the surface inside. To fence a vegetable patch, you need the perimeter (20 m). To know how much soil to spread, you need the area, which you find by multiplying: 6 × 4 = 24 m².

A quick experiment makes this clear. Draw a square on graph paper, 4 squares on each side, and a rectangle 6 squares by 2. Both have the same perimeter: (4 + 4) × 2 = 16 and (6 + 2) × 2 = 16. But the square covers 16 squares, the rectangle only 12. Same perimeter, different areas: proof that these are two separate measurements. For more, our article on the area of a rectangle and square units explains the difference in detail.

If your child is younger, remember it all starts well before the formula: measuring lines, spotting right angles, recognising a rectangle. We cover these basics in our geometry guide for CE2 (age 8-9).

Three activities to practise tonight

1. The string around the garden (or table). Stretch a piece of string all the way round a table or a planter, tie a knot where it meets, then measure the string laid flat. Next, your child measures the length and width and works out (L + w) × 2. The two results should be close: it’s the formula in action, right before their eyes.

2. Walking the edge of the rug. One child walks around a rectangular rug, heel to toe, while another counts the steps. Then count the steps along just one length and one width, and use the formula. If the numbers don’t match exactly, that’s normal: steps aren’t a precise measure, and it’s a good chance to talk about why we use metres.

3. The 20 cm challenge. “Draw a rectangle with a perimeter of 20 cm.” There are several whole-number answers, since the length plus width just needs to make 10: 9 and 1, 8 and 2, 7 and 3, 6 and 4, or 5 and 5 (a square). Finding all the solutions is great practice with half-perimeters, even without naming it.

For more practice, try our printable CM1 exercises for regular training, and a well-designed maths revision sheet to bring perimeter, area and units together on one page before a test.