Area by Tiling
Find the area of a rectangle by tiling it with unit squares and show that the result equals the product of the side lengths
Ce que l'enfant saura faire ensuite
- Tile a 4×6 rectangle and count 24 squares, then verify 4×6=24
- Explain why the number of rows times the number in each row gives the area
- Draw a rectangle on squared paper, tile it, and write the multiplication
1 · Lis
You already know area tells you how much surface a shape covers, measured in square units. One way to find the area of a rectangle is tiling: cover it completely with unit squares, no gaps and no overlaps, then count them.
Leo tiles a rectangle that is 3 squares tall and 5 squares wide. He counts the squares in one row: 5. He has 3 rows just like that one, so the total is 3 x 5 = 15 squares, without counting one by one.
You never have to count every square. Count how many squares are in one row, count the rows, then multiply: rows times squares per row gives the area.
Tiling a rectangle with unit squares shows why its area equals rows times columns, so you can multiply instead of counting one by one.
À lire aussi
Exploring Rectangle Area
Explore area by covering rectangles with squares. Take any rectangle and lay unit squares over it with no gaps. Count the squares: that count is the area. A rectangle 4 squares by 6 squares holds 4 rows of 6, which is 24 squares. Now multiply the side lengths: 4 x 6 = 24. Same answer. That is the big discovery: counting tiles and multiplying sides always agree. Try it on squared paper with your own rectangles and check every time.
Area of rectangles review
Area is the space inside a flat shape. Think of it as how much surface the shape covers. For rectangles there is a shortcut. Count how many unit squares fit in one row. Count how many rows fit. Multiply the two counts. A rectangle with 3 squares in each row and 5 rows has area 3 x 5 = 15 square units. The word square units matters: area counts squares, not lines. Tiling first and multiplying second always give the same number.
How to Find the Area and Perimeter of a Rectangle: 8 Steps
A rectangle has 4 square corners. Its opposite sides match. To find its area, multiply the two different side lengths. A garden 6 m by 4 m has area 6 x 4 = 24 square metres. To find its perimeter instead, add all four sides: 6 + 4 + 6 + 4 = 20 m. Area counts the squares inside, so its units are square metres. Perimeter walks the edge, so its units are plain metres. Never mix the two: multiply for area, add for perimeter.
Pour aller plus loin
2 · Regarde
En anglais3 · Jouer
Tap squares to build a shape, and watch its area and perimeter change.
Sans écran
Où se situe ce sujet
À apprendre avant
Ce sujet mène à
Où cela peut mener
16 questions attendent derrière cette leçon, chacune avec sa réponse expliquée. Chaque réponse nourrit le ciel : les étoiles s'allument à mesure qu'elles sont apprises, et pâlissent quand vient le moment de revenir.