Year 6 Arithmetic (SATs): Area of rectangles and squares, and estimating capacity
Part of the Year 6 Arithmetic (SATs) measures and conversions chapter. Chapter overview · whole chapter on one page
Area of rectangles and squares, and estimating capacity
Rule
The area of a rectangle is length × width, and it is measured in square units, such as cm² or m².
A square has all four sides equal, so its area is side × side.
Key ideas
- Area of a rectangle = length × width.
- Area of a square = side × side.
- Compare areas by working them out, not by comparing the sides.
Method. Multiply length by width.
- Write the formula. Area of a rectangle is length × width.A = l × w
- Multiply. Multiply 7 m by 4 m.7 × 4 = 28
- Write the answer. 28 m²
Check. 28 ÷ 4 = 7. ✓
Watch out. Area is in square metres, m², not metres.
Method. Multiply the side by itself.
- Write the formula. Area of a square = side × side.A = 9 × 9
- Multiply. 9 × 9 = 81.81
- Write the units. Area is in square centimetres.81 cm²
- Write the answer. 81 cm²
Check. 81 = 9 × 9. ✓
Method. Work out both areas, then compare.
- Rectangle. 6 × 5 = 30 m².30 m²
- Square. 6 × 6 = 36 m².36 m²
- Compare. 36 is bigger than 30.the square
- Write the answer. the square
Check. 36 > 30, so the square is bigger. ✓
Exercise 8E Practice: area and capacity
Non-calculatorMethod. Multiply length by width.
- Write the formula. Area of a rectangle is length × width.A = l × w
- Multiply. Multiply 12 cm by 5 cm.12 × 5 = 60
- Write the answer. 60 cm²
Check. 60 ÷ 5 = 12. ✓
Method. Multiply length by width.
- Write the formula. Area of a rectangle is length × width.A = l × w
- Multiply. Multiply 8 cm by 9 cm.8 × 9 = 72
- Write the answer. 72 cm²
Check. 72 ÷ 9 = 8. ✓
Method. Multiply length by width.
- Write the formula. Area of a rectangle is length × width.A = l × w
- Multiply. Multiply 14 cm by 3 cm.14 × 3 = 42
- Write the answer. 42 cm²
Check. 42 ÷ 3 = 14. ✓
Method. Multiply length by width.
- Write the formula. Area of a rectangle is length × width.A = l × w
- Multiply. Multiply 11 cm by 4 cm.11 × 4 = 44
- Write the answer. 44 cm²
Check. 44 ÷ 4 = 11. ✓
Method. Multiply length by width.
- Write the formula. Area of a rectangle is length × width.A = l × w
- Multiply. Multiply 20 cm by 6 cm.20 × 6 = 120
- Write the answer. 120 cm²
Check. 120 ÷ 6 = 20. ✓
Method. Multiply the side by itself.
- Write the formula. Area of a rectangle is length × width.A = l × w
- Multiply. Multiply 7 cm by 7 cm.7 × 7 = 49
- Write the answer. 49 cm²
Check. 7 × 7 = 49. ✓
Method. Multiply the length by the width.
- Write the formula. Area of a rectangle is length × width.A = l × w
- Multiply. Multiply 5 m by 4 m.5 × 4 = 20
- Write the answer. 20 m²
Check. 20 ÷ 4 = 5. ✓
Method. Change 50 cm to 0.5 m, then multiply.
- Change the width. 50 cm = 0.5 m.0.5 m
- Multiply. 2 × 0.5 = 1.1 m²
- Write the answer. 1 m²
Check. 1 m² is the same as 100 cm by 100 cm. ✓
Method. Change the litres to millilitres, then divide by 250.
- Change to ml. 1.5 litres = 1,500 ml.1,500 ml
- Divide. 1,500 ÷ 250 = 6.6
- Write the answer. 6
Check. 6 × 250 = 1,500. ✓
Method. One litre is 1,000 ml, and 1,000 ÷ 250 is 4.
- Change to ml. 1 litre = 1,000 ml.1,000 ml
- Divide. 1,000 ÷ 250 = 4.4
- Write the answer. 4
Check. 4 × 250 = 1,000. ✓
Method. Work out both areas.
- Rectangle. 9 × 4 = 36 cm².36 cm²
- Square. 6 × 6 = 36 cm².36 cm²
- Compare. They are equal, both 36 cm².36 cm²
- Write the answer. 36 cm²
Check. Both areas are 36 cm². ✓
Method. Work out both areas, not just one side.
- Rectangle. 4 × 8 = 32 cm².32 cm²
- Square. 4 × 4 = 16 cm².16 cm²
- Write the answer. No, the rectangle has area 32 cm² and the square has area 16 cm², so they are different.
Check. 32 is not equal to 16. ✓
Method. Change litres to millilitres, then divide by 500.
- Change to ml. 10 litres = 10,000 ml.10,000 ml
- Divide. 10,000 ÷ 500 = 20.20 bottles
- Write the answer. About 10,000 ml, which fills about 20 bottles of 500 ml.
Check. 20 × 500 = 10,000. ✓