Split it into rectangles (the additive method) — draw one internal line, calculate each rectangle's area, then add them together. Any missing side length can usually be found because sides running the same direction must add up to the total: if the full width is $8$ m and one section is $3$ m, the other is $8-3=5$ m.

Example: An L-shaped room has total height $5$ m, total width $8$ m, with a cut-out corner of height $2$ m and width $3$ m.

1. Missing height: $5-2=3$ m. Missing width: $8-3=5$ m.
2. Split into two rectangles: $5\text{ m}\times5\text{ m}=25$ m² and $3\text{ m}\times3\text{ m}=9$ m².
3. Total area: $25+9=34$ m².

Use the subtractive method when the shape is easier to see as a large rectangle with a smaller piece removed — it's often fewer steps than splitting into several positive pieces.

Example: A $2.5$ m $\times 1.2$ m sheet has a $40$ cm $\times 30$ cm rectangular hole cut from a corner.

1. Convert the hole to metres first: $40$ cm $=0.4$ m, $30$ cm$=0.3$ m.
2. Whole sheet: $2.5\times1.2=3.0$ m². Hole: $0.4\times0.3=0.12$ m².
3. Remaining area: $3.0-0.12=2.88$ m².

Treat the semicircle as its own component: find its radius (half of whichever straight edge is the diameter), then use $\frac12\pi r^2$ for its area, and add that to the rest of the shape.

Example: A patio is a $10$ m $\times 5$ m rectangle with a semicircle attached along the $10$ m side.

1. Radius of semicircle: $10\div2=5$ m.
2. Rectangle area: $10\times5=50$ m². Semicircle area: $\frac12\pi(5)^2=12.5\pi\approx39.27$ m².
3. Total: $50+39.27\approx89.3$ m² (3 s.f.).

Multiply the total area by the cost per unit area — but only once every unit matches.

Treat the missing-length deduction exactly as you would with numbers, just using expressions — sides running in the same direction must still sum to the total, which sets up a mini equation to solve.

Example: An L-shape has total width $12$ cm, made up of two sections of width $x$ and $(x+2)$. Since $x+(x+2)=12$, solving gives $2x=10$, so $x=5$ — the two widths are $5$ cm and $7$ cm.

A garden is a $12$ m $\times 9$ m rectangle with a triangular flower bed (base $4$ m, height $3$ m) removed from one corner. Turf costs £4.20 per m². Find the cost of turfing the remaining garden.

1. Rectangle area: $12\times9=108$ m².
2. Triangle area: $\frac12\times4\times3=6$ m².
3. Remaining area: $108-6=102$ m².
4. Cost: $102\times£4.20=£428.40$.