A rectangle without counting
Show on a big screenA store floor has 4 rows of 9 tiles. Each tile is one square. Counting the tiles one by one is slow.
- A rectangle, 9 across and 4 up.
- One row holds 9 squares.
- Four rows, all filled.
- 9 × 4 = 36.
Multiplying is the row count, done fast
Each row holds 9 squares. Four rows hold 9 + 9 + 9 + 9 = 36. Multiplying gives the same: 9 × 4 = 36.
It works when a side is not a whole number. Make the floor 4.5 rows. Four rows hold 4 × 9 = 36 squares. The half row holds 9 ÷ 2 = 4.5. Together that is 36 + 4.5 = 40.5, and 9 × 4.5 = 40.5.
Rule: area of a rectangle = length × width.
Watch out!
A perimeter is the distance round the edge. Two rectangles can share a perimeter and differ in area. 9 by 2 and 6 by 5 both have perimeter 22. Check: 9 + 2 + 9 + 2 = 22 and 6 + 5 + 6 + 5 = 22. Their areas are 18 and 30.
Drag the width from 4 rows to 4.5 rows. Watch the half row appear.
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Try the lab to finish this lesson.