2
Checking a square's area
Discover Mathematics P3: Term 1, Lessons 41–50
GoalFind the area of a square by multiplying the side by itself, and not by adding the sides.
New words
area · the number of square units that cover a shapesquare unit · a square with sides of 1 unit, used to measure areaside · one straight edge of a shape
Explanation
To find the area of a square, we count the unit squares inside it. A square with sides of 4 units has 4 rows with 4 unit squares in each row, so its area is 4 × 4 = 16 square units. A friend may say the area is 4 + 4 = 8. That is a mistake, because adding the sides does not count the squares inside. To check, count all the squares in the grid, or add the rows: 4 + 4 + 4 + 4 = 16. Always write the area with square units.
Worked examples
A square of paper has sides of 3 cm. Its area is 3 × 3 = 9 square cm. Count the squares in the grid to check: 3 rows of 3.
A square courtyard has sides of 6 m. Its area is 6 × 6 = 36 square metres. Its perimeter is a different measure: 6 + 6 + 6 + 6 = 24 m.
| Measure | Number | Unit |
|---|---|---|
| Perimeter | 16 | units |
| Area | 16 | square units |
Class activity
Tile the square. Cut small paper squares of the same size. Use them to cover a bigger square drawn on paper with sides of 5 small squares. Count the tiles in each row and the number of rows. Write the multiplication that gives the area. Try a square with sides of 4 and one with sides of 6.
Practice
1
Find the area of this square.
7 × 7 = 49 square units.
2
A square has sides of 9 cm. What is its area?
9 × 9 = 81 square cm.
3
A square tile has a side of 10 cm. What is its area?
10 × 10 = 100 square cm.
4
A square garden has an area of 64 square metres. How long is one side?
8 m, because 8 × 8 = 64.
5
Farida says a square with sides of 6 units has an area of 12 square units, because 6 + 6 = 12. Do you agree?
No. 6 + 6 only adds two sides. The area is 6 × 6 = 36 square units.