Area and perimeter without mixing them up
Perimeter is the distance around the outside. Area is the space covered. The units tell you which one you are working with.
Two different questions
Perimeter asks how far it is around the edge. Picture walking all the way round a paddock and adding up how far you walked.
Area asks how much surface is covered. Picture painting the paddock and asking how much paint it took.
Same shape, two questions that have nothing to do with each other.
Why area is length times width
Cover the rectangle in squares one centimetre across. A rectangle 8 cm long fits 8 squares along each row, and 5 cm wide means 5 of those rows.
So the count is 5 lots of 8, which is 40. That is all "length × width" is doing: counting the squares without having to draw them.
Units are the clue
Perimeter is a length, so it is measured in centimetres or metres.
Area is a count of squares, so it is measured in square centimetres or square metres — written cm² and m².
That little 2 is a gift. If the answer options carry it, the question wants area, whatever the wording made you think.
Working backwards
Some questions give you the area and one side, and ask for the other. Do not reach for a new method: use the one you have, in reverse.
If the area is 40 cm² and the length is 8 cm, then 8 times something is 40, so the width is 40 ÷ 8 = 5 cm.
Shapes that are not rectangles
An L-shaped garden is not a shape you have a formula for. It is two rectangles that happen to be touching.
Draw a line that cuts it into rectangles, work out the area of each, and add them. Where a side length is missing, you can nearly always find it by subtracting two lengths you do have.
Perimeter is different: you still walk all the way round the outside, and the cut line you drew is not part of the walk. It is a working line, not a fence.
When the units change part-way
A question that gives one side in metres and another in centimetres is not being careless. It is checking whether you noticed.
Convert both to the same unit before you multiply anything. Going to the smaller unit is usually safer, because it avoids decimals.
Then remember what the answer's unit should be: a perimeter is a length, so metres or centimetres; an area is a surface, so square metres or square centimetres. Writing cm where cm² belongs loses the mark even when the number is right.
Worked examples
A rectangle is 8 cm long and 5 cm wide. Find its perimeter and its area.
Perimeter walks all four sides: 8 + 5 + 8 + 5 = 26 cm. A quicker way is to add one long and one short side and double it: (8 + 5) × 2 = 26 cm.
Area counts the squares: 8 × 5 = 40, and the unit is square centimetres.
Answer: Perimeter 26 cm, area 40 cm²
A square has sides of 6 m. What is its area?
A square is a rectangle whose sides match, so it is 6 × 6 = 36. The unit is square metres.
Answer: 36 m²
A rectangle has an area of 24 cm² and is 4 cm wide. How long is it?
Area is length × width, so 4 times the length is 24. That makes the length 24 ÷ 4 = 6 cm. Check it: 6 × 4 = 24. It fits.
Answer: 6 cm
Which needs more fencing: a 10 m by 2 m garden, or a 6 m by 6 m garden?
Fencing goes around the edge, so this is perimeter, not area. The long thin one is (10 + 2) × 2 = 24 m. The square one is (6 + 6) × 2 = 24 m. They need the same fencing — even though the square garden has far more space inside it: 36 m² against 20 m².
Answer: The same: 24 m each
An L-shaped room is made of a 4 m by 5 m rectangle joined to a 4 m by 3 m rectangle. What is its area?
Work out each rectangle separately: 4 × 5 = 20 m² and 4 × 3 = 12 m². Add them, because together they make the whole floor.
Answer: 32 m²
A rectangle is 2 m long and 80 cm wide. What is its area in square centimetres?
The units do not match, so convert first: 2 m is 200 cm. Then multiply 200 × 80.
Answer: 16 000 cm²
A square has a perimeter of 36 cm. What is its area?
A square has four equal sides, so each side is 36 ÷ 4 = 9 cm. Area is side times side.
Answer: 81 cm²
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