Discover Mathematics P4: Term 1, Unit 4, Lessons 1–5
GoalFind the area of rectangles and squares in square units and tell area from perimeter.
New words
area · how much surface a shape coverssquare unit · a square that measures 1 unit on each side, such as 1 cm²formula · a rule written with letters: A = l × w
Explanation
Area tells how much surface a shape covers, for example how many tiles cover a floor. We measure it by counting square units. A square centimetre (cm²) is a square with 1 cm sides, and a square metre (m²) has 1 m sides. For a rectangle, count the rows and the squares in each row: A = l × w. A rectangle 9 cm long and 4 cm wide has A = 9 × 4 = 36 cm². A square with a side of 7 m has A = 7 × 7 = 49 m². Perimeter and area are different. The perimeter is a length around the edge, in cm or m. The area is a surface, in cm² or m². Two rectangles with the same perimeter can have different areas.
Worked examples
Count the squares: 5 columns and 3 rows make 5 × 3 = 15 square units. So A = 15 square units.
A classroom floor is 6 m long and 4 m wide. A = 6 × 4 = 24 m². If one tile covers 1 m², Youssef needs 24 tiles.
Length
Width
Perimeter
Area
7
1
16
7
6
2
16
12
5
3
16
15
4
4
16
16
Rectangles with a perimeter of 16 cm can have different areas: 1 by 7 gives 7 cm², 2 by 6 gives 12 cm², 3 by 5 gives 15 cm² and 4 by 4 gives 16 cm². The same perimeter does not mean the same area.
Class activity
Tile the table. Cut paper squares of 1 cm by 1 cm, or draw them on squared paper. Cover a rectangle of paper 6 cm by 3 cm and count the squares. Then check with 6 × 3. Make a different rectangle with the same area but a different perimeter.
Practice
1
Find the area of a rectangle 9 cm by 4 cm.
9 × 4 = 36 cm².
2
Find the area of a square with a side of 8 m.
8 × 8 = 64 m².
3
A rug is 3 m by 2 m. A room floor is 5 m by 4 m. How many square metres of floor are not covered?
Floor 20 m², rug 6 m², so 20 − 6 = 14 m² are not covered.
4
Which is bigger, the area of a 10 cm by 5 cm rectangle or of a 7 cm by 7 cm square?
Rectangle 50 cm², square 49 cm². The rectangle is bigger.
5
Hana says the area of a square with a side of 5 cm is 20 cm². What did she do wrong?
She found the perimeter (4 × 5). The area is 5 × 5 = 25 cm².
