Stage 5 · Time & measures
Perimeter and area
Perimeter = (length + width) × 2.
How to do it
Method
Perimeter = (length + width) × 2
8 by 5: (8 + 5) × 2 = 26
Another way
Add all four sides
8 + 5 + 8 + 5 = 26
In full
A rectangle's perimeter: two lengths and two widths, so add first, then double: (length + width) × 2. 8 cm by 5 cm → (8 + 5) × 2 = 26 cm. You can also write length + width + length + width, or length × 2 + width × 2: 8 × 2 + 5 × 2 = 26 — the same answer. A square's perimeter is its side × 4. Area is length × width: 8 × 5 = 40 cm²; a square's is side × side. Back the other way: a rectangle's width is its area ÷ its length, 48 ÷ 8 = 6; a square of area 49 has the side that times itself makes 49: 7 × 7 = 49, so 7. Width from the perimeter: the perimeter ÷ 2 is length + width, then take the length: perimeter 30, length 9 → 30 ÷ 2 = 15, 15 − 9 = 6; or take off both lengths first, then halve: 30 − 18 = 12, 12 ÷ 2 = 6 — the same answer. Perimeter is in cm, area in cm².
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Rectangle 4 cm by 3 cm: area = ? cm²
Show the answer and working
Answer: Rectangle 4 cm by 3 cm: area = 12 cm²
Area = length × width: 4 × 3 = 12
Example 2
Rectangle, area 32 cm², length 8 cm: width = ? cm
Show the answer and working
Answer: Rectangle, area 32 cm², length 8 cm: width = 4 cm
Width = area ÷ length: 32 ÷ 8 = 4
Example 3
Rectangle 17 cm by 7 cm: perimeter = ? cm
Show the answer and working
Answer: Rectangle 17 cm by 7 cm: perimeter = 48 cm
Perimeter = (length + width) × 2: 17 + 7 = 24, 24 × 2 = 48
Example 4
Rectangle, perimeter 42 cm, length 11 cm: width = ? cm
Show the answer and working
Answer: Rectangle, perimeter 42 cm, length 11 cm: width = 10 cm
Half the perimeter is length + width: 42 ÷ 2 = 21, then take the length: 21 − 11 = 10
Practise perimeter and area in the game →Stage 5 · Time & measures · Free to start, unlimited questions, no download