What you'll learn
Length is how long something is, measured in millimetres, centimetres, metres or kilometres, and perimeter is the total distance all the way around the outside edge of a flat shape. If you walked right around the edge of your school yard and came back to where you started, the distance you walked is the perimeter. This topic covers choosing the right unit, changing from one unit to another, measuring and estimating sensibly, and working out the perimeter of squares, rectangles, triangles and L-shaped figures — including the harder questions where a side is missing or where the perimeter is given and you must work backwards. Measurement is 9 of the 40 items on the SEA Mathematics paper, and length and perimeter questions appear in almost every sitting, often wrapped up in a real problem about fencing, ribbon or walking to school.
Key terms and definitions
Length — the measurement of how long something is from one end to the other.
Millimetre (mm) — the smallest unit on a school ruler. Ten millimetres make one centimetre.
Centimetre (cm) — the unit used for pencils, exercise books and small objects. One hundred centimetres make one metre.
Metre (m) — the unit used for rooms, fences and playing fields. One thousand metres make one kilometre.
Kilometre (km) — the unit used for the distance between towns, such as Port of Spain to Chaguanas.
Perimeter — the total distance around the outside of a flat (two-dimensional) shape, found by adding the lengths of all its sides.
Regular shape — a shape whose sides are all the same length, such as a square or an equilateral triangle.
Compound shape — a shape made by joining or cutting rectangles, such as an L-shaped room.
Estimate — a sensible guess at a measurement, made without measuring exactly.
Core concepts
The units and how they fit together
There are only four length units you need for SEA, and each one is bigger than the last:
| Unit | Short way | How it relates | Used for |
|---|---|---|---|
| Millimetre | mm | 10 mm = 1 cm | the thickness of a coin |
| Centimetre | cm | 100 cm = 1 m | a pencil, a book, your hand |
| Metre | m | 1 000 m = 1 km | a classroom, a fence, a field |
| Kilometre | km | — | the drive to San Fernando |
The numbers 10, 100 and 1 000 are the only three you have to remember. Everything else follows from them.
Changing from one unit to another
Going from a big unit to a small unit, you multiply, because it takes many small units to make one big one. Going from small to big, you divide.
3 m = 3 × 100 = 300 cm. 4.5 km = 4.5 × 1 000 = 4 500 m. 250 cm = 250 ÷ 100 = 2.5 m. 8 mm = 8 ÷ 10 = 0.8 cm.
The check that saves marks: if you changed to a smaller unit and your number got smaller, you have divided when you should have multiplied. Metres to centimetres must always give a bigger number.
Choosing a sensible unit, and estimating
A door is about 2 m tall, not 2 cm and not 2 km. A pencil is about 15 cm. A grain of rice is a few millimetres. The distance from home to school is given in kilometres if it is a drive and in metres if it is a walk.
Estimating is a real SEA skill. Your finger is roughly 1 cm wide and a big step is roughly 1 m, which lets you estimate almost anything in a room without a ruler.
What perimeter really means
Perimeter is a distance, so the answer always ends in a length unit: cm, m or km — never cm² or m². Those belong to area, which is a different topic.
To find any perimeter, add every side. That rule never fails, even for an odd-looking shape.
For a rectangle there is a shortcut. Opposite sides are equal, so perimeter = (length + width) × 2. A rectangle 9 m long and 4 m wide has perimeter (9 + 4) × 2 = 13 × 2 = 26 m.
For a square all four sides are equal, so perimeter = side × 4. A square with side 7 cm has perimeter 28 cm.
For a triangle, add the three sides. If it is equilateral, multiply one side by 3.
Compound (L-shaped) figures
An L-shaped figure is a rectangle with a smaller rectangle cut out of one corner. You cannot use a single shortcut, so read the sides in order as you travel around the outline and add them all.
Here is one described in words. Start at the bottom left corner and walk: 8 m to the right, 3 m up, 3 m to the left, 2 m up, 5 m to the left, then 5 m down, which brings you back to the start. The perimeter is 8 + 3 + 3 + 2 + 5 + 5 = 26 m.
Notice something useful. The two rightward-and-leftward moves must cancel: 8 to the right, then 3 and 5 to the left, and 3 + 5 = 8. The up-and-down moves must cancel too: 3 up and 2 up is 5 up, and there is 5 down. That is how you find a missing side in an L-shape — the sides going one way must add up to the same total as the sides going the opposite way.
Working backwards from a given perimeter
Some questions give you the perimeter and ask for a side. Undo the shortcut.
A square has perimeter 36 cm, so one side is 36 ÷ 4 = 9 cm.
A rectangle has perimeter 30 cm and length 9 cm. Half the perimeter is one length plus one width, so 30 ÷ 2 = 15 cm, and the width is 15 − 9 = 6 cm. Children who forget to halve first will subtract 9 from 30 and answer 21 cm, which is wider than the whole rectangle is long.
Worked examples
Example 1: Fencing a garden
Anisa's father is fencing a rectangular vegetable garden that measures 12 m by 7 m. Fencing costs TT$25 per metre. How much will the fencing cost?
First find the perimeter: (12 + 7) × 2 = 19 × 2 = 38 m.
Then find the cost: 38 × 25. Split it up — 38 × 20 = 760 and 38 × 5 = 190, so 760 + 190 = TT$950.
The two steps must come in that order. Multiplying 12 × 25 and 7 × 25 and stopping there gives the cost of only two sides.
Example 2: The perimeter of an L-shaped room
Kern's grandmother has an L-shaped verandah. Walking around the edge, the sides in order are 9 m, 4 m, 4 m, 3 m, 5 m and 7 m. She wants to run decorative rope right around the edge. How much rope does she need?
Add every side in order: 9 + 4 = 13, 13 + 4 = 17, 17 + 3 = 20, 20 + 5 = 25, 25 + 7 = 32 m.
Check that the shape closes. The horizontal sides are 9 one way against 4 and 5 the other way, and 4 + 5 = 9. The vertical sides are 4 and 3 one way against 7 the other way, and 4 + 3 = 7. Both directions balance, so the six sides really do make a closed L.
She needs 32 m of rope.
Example 3: Laps of the field, with a unit change
The school field is a rectangle 120 m long and 80 m wide. Devon runs three complete laps around the edge. How far does he run, in kilometres?
One lap is the perimeter: (120 + 80) × 2 = 200 × 2 = 400 m.
Three laps: 400 × 3 = 1 200 m.
The question asks for kilometres, so divide by 1 000: 1 200 ÷ 1 000 = 1.2 km.
Two things are tested at once here: the perimeter and the unit change. Writing 1 200 km would lose the mark even though the hard part was done correctly.
Common mistakes and how to avoid them
Adding only two sides of a rectangle. Working out 12 + 7 = 19 and calling that the perimeter. Fix: say out loud, "a rectangle has four sides," and double the total.
Mixing units in one sum. Adding 2 m and 50 cm to get 52. Fix: change everything to the same unit first — 200 cm + 50 cm = 250 cm, which is 2.5 m.
Dividing when you should multiply. Turning 3 m into 0.03 cm. Fix: a smaller unit must give a bigger number.
Forgetting a side of an L-shape. Adding five sides when there are six. Fix: touch each side with your pencil as you add it, and check that the horizontal sides balance and the vertical sides balance.
Writing a square unit for perimeter. Answering 26 m². Fix: perimeter is a walk around the edge, so it is measured in plain metres.
Not halving first when the perimeter is given. Fix: half the perimeter is one length plus one width.
How parents can help at home
You do not need to remember any of this yourself to be useful — you only need to keep asking for measurements.
Give your child the tape measure. Ask for the length of the kitchen counter, the height of the doorway, the width of the fridge. Then ask the follow-up question: "and how much is that in metres?" Changing units is the part that slips, and it only becomes automatic through repetition.
Ask for an estimate before the measurement. "How wide do you think this table is?" Then measure. Being close is a real skill, and being wildly out is a useful surprise.
Walk a perimeter. Walk around the yard together, counting big steps as roughly one metre each, and ask for the total distance.
When your child is stuck, the prompt is almost always "write down every side, then add them." If the shape is an L, add: "read the sides in order, as though you are walking around it." Most errors in this topic are missed sides, not wrong arithmetic.
At the shop, ribbon and rope are sold by the metre, so ask what it would cost to go right around something at the marked price per metre.
Exam technique for length and perimeter
Underline the unit the question wants before you start. Many SEA items give the measurements in metres and ask for the answer in kilometres, or give centimetres and ask for metres. The arithmetic is easy; the unit is where the mark is lost.
Convert first, calculate second. If one side is given in metres and another in centimetres, change them both before adding anything.
For any shape that is not a plain rectangle or square, list the sides in a column and add them down the page. It is slower than trying to do it in your head, and it is far more accurate.
Check your answer for sense. A perimeter must be bigger than the longest single side, and for a rectangle it must be less than four times the longest side. An answer outside that range is wrong.
In multiple-choice items the wrong options are built from the usual errors: half the true perimeter, only two sides added, or the right number with the wrong unit.
Quick revision summary
- 10 mm = 1 cm, 100 cm = 1 m, 1 000 m = 1 km.
- Big unit to small unit: multiply. Small unit to big unit: divide.
- Perimeter is the distance all the way around, so add every side.
- Rectangle: perimeter = (length + width) × 2. Square: perimeter = side × 4.
- L-shapes: add all six sides; the horizontal sides balance and the vertical sides balance.
- Given the perimeter of a rectangle, halve it first to get one length plus one width.
- Perimeter is a length, so the unit is m or cm, never m² or cm².
- Convert to a common unit before adding, and answer in the unit the question asks for.