Rectangle area

1Summary 重點摘要

Area = length × width.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Part 1: Start by counting squaresA rectangle 6 cm long and 4 cm wide fits 6 one-square-centimetre tiles in each row, with 4 rows in all: 6 + 6 + 6 + 6 = 24 tiles. Those 24 squares are exactly the area of the rectangle, 24 cm². Why little squares? Area is the number of squares needed to cover the shape, which is the very meaning of area. Take care that the tiles must cover the shape fully without overlapping; 6 tiles a row and 4 rows, every row counted in full, for one row missed spoils the total.
2. Part 2: Counting becomes multiplying6 + 6 + 6 + 6 is four sixes added, written as 6 × 4 = 24, and so counting tiles upgrades into a formula. The rectangle area formula is length × width. By the formula, 6 × 4 = 24 cm², exactly the same result as counting tile by tile. Why can the formula be trusted? Tiles per row give the length, the number of rows gives the width, and multiplying gives all the tiles. Take care that length and width must share one unit; one in cm and one in m makes the product completely wrong.
3. Part 3: Squares are a special caseA square with side 5 cm has the same length and width, so area = 5 × 5 = 25 cm². A square is a rectangle whose sides are equal, so its area formula can be written as side × side, a number multiplied by itself. Why is the square a special case? Length equals width, and the formula shrinks to one number times itself. Take care that 5 × 5 may also be written 5², read five squared; the two forms are equivalent, but at primary level 5 × 5 is the clearest and least open to misunderstanding.
4. Part 4: The unit must be squareLength is measured in cm, but area comes from cm × cm, so the unit is written cm², read square centimetres. Area 24 cm² must not be written as 24 cm; without the square it reads as a length and is incomplete. Why does the unit carry a square? Two length units multiply together, and cm × cm is cm², for the units multiply along with the numbers. The usual error is finding the right number in a word problem but leaving out the unit, or writing cm instead of cm²; a right number with a wrong unit is still not a correct answer.
5. Part 5: Finding a missing sideGiven area 24 cm² and length 6 cm, find the width. Because 6 × width = 24 and division undoes multiplication, width = 24 ÷ 6 = 4 cm. Check with 6 × 4 = 24, which matches the area, so the answer is right. This kind of question runs the formula backwards. Take care to tell the length from the area; dividing the area by the length gives the width, while multiplying the two known numbers reverses the direction completely and produces the absurd 144, which a single check exposes.
6. Part 6: Everyday useA basketball court 28 m long and 15 m wide has area 28 × 15 = 420 m². A room 4 m by 3 m has area 12 m², which is exactly the figure to use when buying flooring. Measure length and width, and any rectangle's area follows. Take care to check the units agree in real-life problems; when the length is in m and the width in cm, convert to one unit before multiplying, for multiplying across mismatched units gives a result out by a hundred times, and the material is bought wrong.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Rectangle area = length × width
• Square area = side × side
• Area units are cm² and m², never cm
• Missing side: divide, width = area ÷ length
• 1 m² = 10000 cm²