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
کارهایی که یادگیرنده بعد از این درس می‌تواند انجام دهد
- 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
۱ · بخوان
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.
برای خواندن بیشتر
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.
کاوش بیشتر
۲ · ببین
به انگلیسی۳ · بازی
Tap squares to build a shape, and watch its area and perimeter change.
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