Rectangle area and perimeter:
two measurements that answer different questions

Cover it or fence it: which measurement do you need?

Both measurements describe the same rectangle but answer different questions. Area is how much flat surface lies inside the shape. You use it to buy paint, tiles, carpet, turf or fertiliser. Perimeter is the distance around the outside. You use it to buy fencing, skirting, trim or a border strip.

A quick test: if the material comes in rolls, sheets or bags that spread over the surface, you want area. If it runs along the edge in a line, you want perimeter. Getting this backwards is the most common slip, and the numbers can look plausible enough that nobody notices until the order arrives.

The two formulas

Both formulas assume the corners are right angles. If the shape is a parallelogram or has been measured at a slant, the area is base × perpendicular height, not base × slanted side.

Worked example: a 12 m by 8 m plot

If tiles cover 0.5 m² each, you need 96 ÷ 0.5 = 192 tiles before wastage. If fencing is sold in 2.5 m panels, you need 40 ÷ 2.5 = 16 panels. The same rectangle produced a tile count and a panel count, each from a different formula.

Order extra for cuts and breakage. A margin of 5% to 10% is common for tiles, depending on the pattern, but check with the supplier.

The units trap: why area is in squares

Area is a count of unit squares, so the unit is squared. Multiply metres by metres and you get square metres. Multiply a measurement in metres by one in centimetres and the result means nothing until you convert one of them.

Notice that 1 m² is 10,000 cm², not 100. A length converts by a factor of 100, but an area converts by that factor squared. Forgetting this makes a room look a hundred times smaller than it is.

Same perimeter, very different area

Perimeter does not fix area. Take a fixed 40 m of fencing and see how much ground it can enclose.

The square encloses the most. As the rectangle gets longer and thinner the area falls away even though the fence is the same length. This is why a long narrow plot at the same perimeter holds less usable land.

A room worked through: floor, skirting and paint

Take a living room that is 5.4 m long and 3.8 m wide with a 2.7 m ceiling and one 0.9 m doorway. The floor, the skirting and the walls each need a different measurement from the same two numbers.

The wall figure is a perimeter multiplied by a height. A room is four rectangles standing on the floor, and their total width is exactly the perimeter. It is a handy trick: the perimeter times the height gives the wall area in one step.

Paint is sold by coverage, which depends on the surface and the product, so divide the wall area by the coverage on the tin and round up. Two coats double the quantity.

When the shape is not quite a rectangle

Real rooms have alcoves, bay windows and cut-off corners. The trick is to carve the outline into rectangles and treat each one separately.

• L-shaped room: split it into two rectangles, find each area and add them. Alternatively take a big rectangle and subtract the missing corner.
• Perimeter of an L-shape: add every outer edge. It equals the perimeter of the bounding rectangle, because the notch swaps edges of the same total length.
• Rectangle with a square cut-out: subtract the cut-out's area but add its edges to the perimeter if the inner edge also needs fencing or trim.
• Nearly-rectangular plots: measure both pairs of opposite sides and both diagonals. If the diagonals differ, the corners are not square and the simple formula will be off.

A land plot described in a document may use a different unit from the one you measured, such as acres, gunthas, cents or square yards. Convert once into square metres or square feet and keep working in that unit.

Checking your answer before you buy

• Measure the room's longest and shortest runs at the widest points, not along one wall only.
• Write the unit next to every number so that a square unit is never confused with a plain one.
• Sanity-check: area should be roughly length times width, so a 4 m by 5 m room cannot be 90 m².
• For L-shaped or irregular rooms, split into rectangles, find each area, then add them.
• Subtract doors and windows from wall area for paint or wallpaper, but not from floor area unless the space will really be left untiled.

A rectangle calculator is handy for checking the multiplication and for converting a perimeter back into side lengths when you know one side and the total fence.