Perimeter and area · Usually met around P4
Perimeter and area of rectangles and squares
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 has two lengths and two widths. So for its perimeter, add first, then double: (length + width) × 2. 8 cm by 5 cm → (8 + 5) × 2 = 26 cm. You can also do length + width + length + width, or length × 2 + width × 2: 8 × 2 + 5 × 2 = 26. A square's perimeter is its side × 4. Area is length × width: 8 × 5 = 40 cm². A square's area is side × side. To go backwards, a rectangle's width is its area ÷ its length: 48 ÷ 8 = 6. For a square with an area of 49, find the number that times itself makes 49: 7 × 7 = 49, so the side is 7. To find the width from the perimeter, halve the perimeter to get length + width, then take away the length: perimeter 30, length 9 → 30 ÷ 2 = 15, 15 − 9 = 6. Or take away both lengths first, then halve: 30 − 18 = 12, 12 ÷ 2 = 6. Perimeter is in cm, and area is in cm².
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Square, side 6 cm: area = ? cm²
Show the answer and working
Answer: Square, side 6 cm: area = 36 cm²
A square's area is side × side: 6 × 6 = 36
Example 2
Square, area 144 cm²: side = ? cm
Show the answer and working
Answer: Square, area 144 cm²: side = 12 cm
Which number times itself makes 144? 12 × 12 = 144, so the side is 12
Example 3
Rectangle 5 cm by 2 cm: perimeter = ? cm
Show the answer and working
Answer: Rectangle 5 cm by 2 cm: perimeter = 14 cm
Perimeter = (length + width) × 2: 5 + 2 = 7, 7 × 2 = 14
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