GoalFind the area of a rectangle by counting square tiles and by multiplying rows by tiles in a row.
New words
area · the amount of flat space a shape coverssquare tile · a square used to measure arearow · a line of tiles going across
Explanation
Area tells us how much flat space a shape covers. We measure it by covering the shape with equal squares that leave no gaps and do not overlap, and then counting the squares. A rectangle of tiles is an array. If it has 3 rows with 4 tiles in each row, the area is 3 × 4 = 12 square tiles. Counting every tile one by one is slow, and it is easy to count a tile twice or to miss one. It is better to count one row and then multiply by the number of rows. Always write the area with its unit, such as 12 square tiles.
Worked examples
A floor has 3 rows with 10 tiles in each row. The area is 3 × 10 = 30 square tiles. If someone counts 31, a tile was counted twice, often the corner tile where two rows meet.
Seif tiles a balcony with 4 rows of 7 tiles. The area is 4 × 7 = 28 square tiles. We can check by turning the rectangle: 7 rows of 4 also gives 7 × 4 = 28.
Rows
Tiles in a row
Area
1
12
12
2
6
12
3
4
12
The same 12 tiles can make different rectangles, but the area is always 12 square tiles.
Class activity
Tile hunt. Find a tiled floor or wall at home. Choose a part with at most 5 rows. Count the tiles in one row and the number of rows, then multiply to find the area of that part. Count the tiles one by one to check. Which way was faster?
Practice
1
A rectangle of tiles has 2 rows with 9 tiles in each row. Find its area.
2 × 9 = 18 square tiles.
2
Count the rows and the tiles in a row. What is the area of this rectangle?
There are 3 rows with 5 tiles in each row, so the area is 3 × 5 = 15 square tiles.
3
Salma counts a rectangle of 6 rows with 5 tiles in each row and says the area is 31. Is she right?
No. 6 × 5 = 30, so the area is 30 square tiles. She probably counted one tile twice.
4
A kitchen floor is 8 tiles long and 6 tiles wide. How many tiles cover it?
8 × 6 = 48 square tiles.
5
Omar says a rectangle of 7 rows with 7 tiles in each row has an area of 14. What did he do wrong?
He added 7 + 7 instead of multiplying. The area is 7 × 7 = 49 square tiles.
