Perimeter

1Summary 重點摘要

Distance around shape. Rectangle = (L+W)×2.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Part 1: Perimeter is one loop aroundWalk once around the edge of a rectangle; the total distance covered is its perimeter. You could also wrap string around the shape, cut it off and measure — the length of the string is the perimeter. It measures the rim, not the space inside. Telling perimeter from area is the first lesson of measuring shapes; their units differ too — perimeter uses length units like cm and m.
2. Part 2: The basic method: add every sideA triangle with sides 3 cm, 4 cm and 5 cm has perimeter 3 + 4 + 5 = 12 cm. This method works for every shape: add up the lengths of all the sides, missing none, and the total is the perimeter. For shapes with many sides, group the equal sides first and then add them — quicker and safer from omissions.
3. Part 3: The rectangle shortcutA rectangle 5 cm long and 3 cm wide: two lengths plus two widths give 5 + 3 + 5 + 3 = 16 cm. Since length and width each appear twice, write (5 + 3) × 2 = 16 cm. The formula is: rectangle perimeter = (length + width) × 2. Before using the formula, confirm the two sides share one unit; different units cannot be added directly.
4. Part 4: Squares and regular shapesA square's four sides are equal, so with side 4 cm its perimeter is 4 × 4 = 16 cm. An equilateral triangle's three sides are equal, so with side 6 cm its perimeter is 6 × 3 = 18 cm. When all sides match, multiply one side by the number of sides. Count the sides first, then multiply — the order least likely to go wrong.
5. Part 5: Working backwardsA square has perimeter 20 cm; since perimeter = side × 4, the side = 20 ÷ 4 = 5 cm. A rectangle has perimeter 16 cm and length 5 cm: first 16 ÷ 2 = 8 gives length plus width, then 8 − 5 = 3, so the width is 3 cm. Working backwards turns the formula around; division and subtraction each mirror one step of it, so keep the reasoning clear.
6. Part 6: Everyday useA flower bed 8 m long and 3 m wide needs at least (8 + 3) × 2 = 22 m of fencing. Photo frame edges, one lap of the track, court boundary lines — all of these are perimeter questions. Name the shape first, then choose the right formula. Always attach the length unit to the answer; in word problems a missing unit counts as incomplete, so make it a habit.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Perimeter = the total border length
• Basic method: add every side
• Rectangle: (length + width) × 2
• Square: side × 4
• Perimeter uses cm/m — different from area in cm²