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This page sets out the method for area & perimeter in the order you would use it, then walks through the full lesson explanation. For three complete worked examples with the slips that cost marks, see the Area & perimeter topic page.
When you see a single shape with lengths marked, name the shape and write its area formula first.
When you see an L-shape or a shape with a piece missing, split it into rectangles or subtract the missing piece.
Add every outside edge.
A 6 by 4 rectangle has perimeter 6 + 4 + 6 + 4 = 20.
Area of a rectangle is length times width.
6 × 4 = 24 square units. Do not add for area.
Perimeter is in cm or m. Area is in cm² or m².
The square on the unit tells you it is area.
Area of a triangle is half of base times height.
The height is perpendicular to the base, not a sloping side.
If the perimeter and three sides are known, subtract to find the fourth.
Then you can find the area if it is a rectangle.
A larger perimeter does not always mean a larger area.
A long thin rectangle can have a big perimeter and a small area.
To find a perimeter, walk around the boundary and add every outside edge once. A rectangle has two lengths and two widths. If the length is 11cm and the width is 4cm, the perimeter is 11+4+11+4=30cm, which is the same as 2×(11+4)=30cm. Do not multiply the length by the width and call that the perimeter. Multiplication gives the area.
Sometimes the perimeter is given and a side is missing. The perimeter of a rectangle is 36cm and the length is 11cm. The two lengths use 2× 11=22cm, so the two widths share 36-22=14cm. Each width is 14÷ 2=7cm. You can write that in one line as (36-2× 11)÷ 2=7. Once the width is known, the area is a separate step: 11× 7=77cm^2.
Method: 1. Add every outside edge once, or use 2×(length+width). 2. A 11cm by 4cm rectangle has perimeter 2×(11+4)=30cm. 3. If the perimeter is 36cm and the length is 11cm, each width is (36-2× 11)÷ 2=7cm.
A rectangle is a grid of unit squares. If one side is 9cm and the other is 6cm, there are 9 rows of 6 squares, or 6 rows of 9 squares. Either way the area is 9× 6=54cm^2. The order of multiplication does not matter. The sides you multiply must meet at a corner. You do not multiply the perimeter by anything to get the area.
The same rectangle has perimeter 2×(9+6)=30cm. Notice that 30 and 54 are different numbers with different units. A square is a rectangle with equal sides, so a square of side 4cm has area 4× 4=16cm^2 and perimeter 4× 4=16cm. Here the numbers match by chance and the units still do not. Always write cm or cm^2 so the two measures stay distinct.
Method: 1. Multiply the two sides that meet at a corner. 2. A 9cm by 6cm rectangle has area 9× 6=54cm^2. 3. A square of side 4cm has both area and perimeter equal to 16, but the units are cm^2 and cm.
Any triangle is half a rectangle that has the same base and the same perpendicular height. The rectangle would have area base × height, so the triangle has area 1/2× base × height. A triangle with base 12cm and perpendicular height 7cm has area 1/2× 12× 7=42cm^2. Halving at the start or at the end is the same: 12× 7=84, then half of 84 is 42.
The height must be perpendicular to the base you chose. On a right-angled triangle the two sides that form the right angle can be the base and the height. On a slanted triangle the height is often drawn outside the triangle or from a vertex down to an extension of the base. A sloping side is not the height, even if it is the only other number printed. If the base is 10cm and the slant is 8cm but the perpendicular height is 6cm, the area is 1/2× 10× 6=30cm^2, not 1/2× 10× 8.
Method: 1. Multiply the base by the perpendicular height, then halve: 1/2×base×height. 2. Base 12cm and height 7cm give 1/2× 12× 7=42cm^2. 3. Use the perpendicular height, so base 10cm and height 6cm give 1/2× 10× 6=30cm^2.
Length is measured in cm, m or mm. Area is measured in cm^2, m^2 or mm^2 because you multiply two lengths. A square that is 1m along each side contains 100× 100=10000 squares that are 1cm along each side, so 1m^2=10000cm^2. That is why you cannot turn an area into another area unit by multiplying by 100 the way you turn metres into centimetres.
Check the unit at the end of every question. Perimeter stays in cm or m. Area is written with a squared unit. If you added the sides, you were finding a perimeter. If you multiplied two perpendicular lengths, or took half of that product for a triangle, you were finding an area. A rectangle of 8cm by 5cm is a useful check pair: perimeter 26cm, area 40cm^2.
Method: 1. Keep perimeter in cm and area in cm^2. 2. Change area units by squaring the length factor: 1m^2=100× 100=10000cm^2. 3. Check a 8cm by 5cm rectangle: perimeter 26cm, area 40cm^2.
An L-shape is two rectangles joined, or one big rectangle with a corner taken away. To find its area, either split it into two rectangles and add, or find the big rectangle and subtract the missing corner. Both methods give the same answer, so pick the one that needs fewer new lengths. Write the area of each part on its own line.
For the perimeter, walk all the way round the edge and add every edge, including the ones you had to work out. A missing length is found by subtraction: if the long side is 12 m and part of it is 5 m, the other part is 7 m. A neat fact helps: cutting a rectangle out of a corner does not change the perimeter.
Method: 1. Mark every missing length on the diagram, using subtraction. 2. For area, split into rectangles and add, or subtract the missing corner. 3. For perimeter, add all the outside edges, counting each one once. 4. Write the units: cm or m for perimeter, and cm squared or m squared for area.
Tip: The inside edges of a split are not part of the perimeter. Only the outside counts.
The area of a parallelogram is the base multiplied by the perpendicular height, A=b× h. The perpendicular height meets the base at a right angle. It is not the sloping side. A parallelogram with base 9.5 cm and height 6 cm has area 9.5× 6=57 cm^2. Questions often include a slanted side as a distraction, so choose the height by looking for the right angle symbol.
A trapezium has one pair of parallel sides. Its area is half the sum of the parallel sides multiplied by the perpendicular distance between them, A=tfrac12(a+b)h. With parallel sides 8 cm and 14 cm and height 6 cm the area is tfrac12× 22× 6=66 cm^2. Always add the parallel sides first and halve afterwards. If you forget the half, check your answer: a trapezium is always smaller than the rectangle drawn around it.
Method: 1. Pick out the base and the perpendicular height, not the slanted side. 2. For a trapezium, find the two parallel sides and add them. 3. Multiply by the height, then halve for a trapezium. 4. Write the answer in square units.
Exam questions often label the sides with expressions. If a rectangle has length (2x+3) and width x, its perimeter is 2×(2x+3+x)=2(3x+3)=6x+6. If the question tells you the perimeter is 36 cm, put 6x+6=36 and solve to get x=5. Then go back and work out the actual lengths and the area. Keep each step on its own line so that an error is easy to find and the method marks are safe.
Take care to answer the question that is asked. The value of x is often an in-between step, and the answer wanted is a length or an area. Check by adding the sides again. For harder questions the area is given instead, which produces a quadratic equation such as x(x+6)=135. Expand, rearrange to zero and solve, then reject any negative length.
Method: 1. Write the perimeter or area as an expression in x. 2. Set it equal to the given value and solve. 3. Substitute back to find each side length. 4. Answer the question asked and check by recalculating the perimeter or area.
Real contexts add a second step. A floor needs tiles, a wall needs paint, a lawn needs seed. First find the area, then divide by the area one tile or one litre covers, or multiply by the cost per square metre. Read the question for rounding: tiles and tins are whole things, so a part of one still has to be bought as a whole one.
Watch the units. One square metre is 100× 100=10 000 cm^2, not 100 cm^2. A rectangle 300 cm by 200 cm has area 60 000 cm^2, which is 6 m^2. The easiest way to avoid the trap is to change both lengths to metres first, giving 3 m× 2 m=6 m^2. If you meet a question with centimetres and metres mixed, change everything to one unit before you multiply anything together.
Method: 1. Convert all lengths to the same unit before multiplying. 2. Work out the area, then divide or multiply for the context. 3. Round up if you need whole tiles, tins or packs. 4. Give the final answer in the unit asked for, such as pounds or square metres.
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