Area of a rectangle
A = l × w (length times width).
A 6 cm by 4 cm rectangle has an area of 24 cm².
Study Resources
Maths Knowledge
Key formulas and methods that come up again and again in NAPLAN Numeracy and Mathematical Reasoning, each with a worked example.
Area and perimeter
Area of a triangle
A = ½ × b × h (half the base times the height).
A triangle with base 10 m and height 6 m has an area of 30 m².
Perimeter
The total distance around the outside of a shape. Add up every side.
A 6 cm by 4 cm rectangle has a perimeter of 6 + 4 + 6 + 4 = 20 cm.
Fractions, decimals and percentages
Percent means “out of 100”
To find a percentage of an amount, divide by 100 and multiply by the percentage.
25% of 80 = 80 ÷ 100 × 25 = 20.
Converting fractions
Divide the numerator by the denominator to get a decimal, then multiply by 100 for a percentage.
3/4 = 3 ÷ 4 = 0.75 = 75%.
Comparing fractions
Rewrite the fractions with the same denominator, then compare the numerators.
3/4 = 9/12 and 2/3 = 8/12, so 3/4 is larger.
Problem-solving methods
Order of operations
Brackets first, then × and ÷ from left to right, then + and − from left to right.
3 + 4 × 2 = 3 + 8 = 11.
Angles in a triangle
The three angles inside any triangle add up to 180°.
If two angles are 50° and 60°, the third is 180 − 110 = 70°.
Work backwards
When you know the result, undo each step in reverse order to find the start.
A number doubled, then add 3, gives 15. Undo: 15 − 3 = 12, 12 ÷ 2 = 6.