Perimeter: walk around a shape · 마틴과 코딩하기

Perimeter: the path all the way round

Imagine an ant that walks around your notebook all the way round along the edge. The path it walked is the perimeter — the sum of the lengths of all the sides of a shape.

You need perimeter whenever you edge something: a fence around a garden, a decorative ribbon around a card, a frame around a picture. The question is always the same: how much do I need all the way round?

With a rectangle (the shape of a notebook: two longer sides, two shorter) you can add all four sides. But there is a shortcut: opposite sides are the same length, so it is enough to add the length and the width and double the result.

With a square all four sides are the same — the perimeter is four times the side.

We write it with the letter o and it is a length, so it has a unit: centimetres, metres… The units from the last lessons have just come in handy.

Sofie is making a card for grandma and wants to edge it with gold ribbon. The card is a rectangle: 15 cm by 10 cm. How much ribbon to cut? Sofie first adds the sides one by one: 15 + 10 + 15 + 10. Then she notices that the pairs repeat: 15 + 10 is 25, and that twice — 50 cm. She cuts 50 cm and the ribbon wraps the card exactly. “Next time I do not have to measure along the sides,” she says to herself, “length and width are enough.”

💡

Before you calculate, run a finger around the shape all the way round and at each side say its length. What the finger walked belongs in the perimeter — and you see at once if you are forgetting a side.

Formulas for a rectangle and a square

A rectangle with sides a (length) and b (width):

Add neighbouring sides: a + b.
Double: o = 2 × (a + b).

Example: a = 6 cm, b = 4 cm → o = 2 × (6 + 4) = 2 × 10 = 20 cm.

The bracket here does exactly what you learned in the ninth lesson: first add, then multiply. Without the bracket (2 × 6 + 4 = 16) you would only double the length — and the ant would run out of path halfway.

A square with side a:

o = 4 × a.

Example: a = 5 cm → o = 4 × 5 = 20 cm.

Method for every perimeter problem:

Draw the shape (from the hand is enough) and label the sides with numbers.
Check the units — all sides the same! (Metres with centimetres convert first.)
Put into the formula and calculate.
Write the result with a unit.

When the shape is not a rectangle or a square — say a triangle or a wiggly plot — do not look for a formula: just add all the sides. Perimeter is always only the path all the way round.

Ribbon around a card

The card is a rectangle 15 cm × 10 cm. How much ribbon for edging?

Step 1: sketch, sides 15 and 10.

Step 2: units the same (cm). Good.

Step 3: o = 2 × (15 + 10) = 2 × 25 = 50 cm.

Check along the sides: 15 + 10 + 15 + 10 = 50. It fits — the formula is just a shortcut for walking all four sides.

A fence around a square bed

The bed is a square with side 3 m. How many metres of fence to buy?

Step 1: a square, all sides 3 m.

Step 2: o = 4 × 3 = 12 m.

And an extra: netting is sold by whole metres at 90 Kč/m. How much do you pay? 12 × 90 = 12 × 9 × 10 = 1 080 Kč. Perimeter is rarely the last question — you usually calculate on with it at once.

Watch the units

A rectangular table has length 1 m and width 60 cm. What is its perimeter?

Trap: 1 + 60 = 61 would be nonsense — I add metres with centimetres.

Step 1: I convert: 1 m = 100 cm.

Step 2: o = 2 × (100 + 60) = 2 × 160 = 320 cm.

Step 3: mixed: 320 cm = 3 m 20 cm.

Units first match, then calculate — the same rule as with weighing.

⚠️

Do not forget the bracket! The perimeter of a rectangle is 2 × (a + b). Whoever writes 2 × a + b doubles only one side — for a rectangle 6 × 4 they get 16 instead of 20 and the fence will not close.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. 시작 with ten. When it goes well, add more.

Perimeters of rectangles: add the sides, double.

Practise the questions

On paper

Draw, measure, calculate. Perimeter is learned with the hands.

Draw a rectangle 8 cm × 5 cm. Work out the perimeter with the formula and then check by adding all four sides.
Measure your notebook with a ruler (round to whole cm) and work out its perimeter.
Work out: the perimeter of a square with side 7 cm, the perimeter of a rectangle 12 m × 9 m, the perimeter of a rectangle 2 m × 80 cm (watch the units!).
The other way: a square has perimeter 36 cm. How long is one side? (Hint: the perimeter is four equal sides — divide.)

Now you 💪

You can say in your own words what perimeter is (the path all the way round, the sum of the sides).
You work out the perimeter of a rectangle 6 × 4 with a bracket: 2 × (6 + 4) = 20.
Before calculating you match the units of all sides.

✅

Done when: You work out the perimeter of a rectangle and a square, you watch the bracket and the units, and you can do the problem the other way too.

What to take from this lesson

Perimeter = the sum of the lengths of all sides. It is written o and has a length unit.
Rectangle: o = 2 × (a + b). The bracket is required.
Square: o = 4 × a.
Before calculating, convert all sides to the same unit.
Unknown shape? No science — add all the sides all the way round.