These questions ask you to find a whole boundary, recover a missing side from a perimeter, or reason about a boundary after a shape changes. Imagine tracing the outside edge and account for every segment you travel.
Choose a boundary method
| Shape or task | Method and tiny example |
|---|---|
| Rectangle | Add two lengths and two widths, or use 2 times the sum of length and width. For 11 cm by 4 cm, the perimeter is 2 times 15 cm, which is 30 cm. |
| Four equal sides | Multiply one side by 4. A shape with four equal sides of 5 cm has perimeter 4 times 5 cm, which is 20 cm. |
| Triangle or irregular polygon | Add every stated side once. Sides of 3 cm, 4 cm and 6 cm give 13 cm. Keep a count so no edge is skipped. |
| Regular polygon | Multiply one side by the number of sides. A regular hexagon with side 3 cm has perimeter 6 times 3 cm, which is 18 cm. |
| Reverse rectangle or four-equal-sided problem | A rectangle's half-perimeter is one length plus one width; when all four sides match, one side is the perimeter divided by 4. From a rectangle perimeter of 34 cm, one length plus one width is 17 cm. |
| Repeated unknown sides | Remove known sides, then share the remainder among equal unknown sides. If 29 cm remains for two equal sides, each is 14.5 cm. |
For a stepped or cut shape, trace the new outline segment by segment. Do not guess from the amount of space inside. If one side is a multiple of another, convert the half-perimeter into equal shares: when a length is three times a width, one length plus one width contains four width-sized shares.
Where boundary calculations go wrong
| Trap | How to reject it |
|---|---|
| Multiplying length by width | That calculation measures the surface inside a rectangle. Perimeter follows the edge, so add the side lengths with their repeated copies. |
| Using four sides for every regular polygon | The multiplier is the shape's actual side count. A triangle uses three, a pentagon five, and a hexagon six. |
| Stopping at the half-perimeter | One length plus one width covers only half a rectangle's boundary. Check whether the question wants that pair or the complete trip around the shape. |
| Keeping a remainder that belongs to two equal sides | After removing the known side, label how many equal sides remain. Divide their combined length before naming one side. |
| Assuming less area always means less perimeter | Area and boundary length measure different features. Trace any replacement edges after a cut instead of predicting the perimeter from the smaller interior. |
Try it
A triangle has sides of 7 centimetres, 9 centimetres and 12 centimetres. Enter the number of centimetres in its perimeter.
A rectangle has a perimeter of 30 centimetres, and one of its sides measures 9 centimetres. How long is the side next to it?
- 6 centimetres
- 12 centimetres
- 15 centimetres
- 21 centimetres
A rectangle has a perimeter of 24 centimetres, and its length is exactly twice its width. Select all the statements that are true about this rectangle.
- The width is 4 centimetres.
- The length is 8 centimetres.
- The width is 8 centimetres and the length is 4 centimetres.
- The width is 6 centimetres and the length is 12 centimetres.