Perimeter is the total distance around the outside of a shape — a one-dimensional length (mm, cm, m). Area is the amount of space enclosed within that boundary — a two-dimensional measure (cm², m²). Confusing the two (applying an area formula where perimeter is needed, or vice versa) is the single most common error on this topic.

The Foundation Tier formulae sheet provides the trapezium area formula, but it deliberately omits the rectangle, triangle and parallelogram formulas — these must be memorised:

Split the shape into rectangles and triangles you recognise, find each area separately, then add them together. For shapes with a missing length, express the area as an algebraic expression in terms of that length, set it equal to the total area given, and solve.

A classic Foundation question gives one shape's perimeter and asks about a different shape's area.

Example: a rectangle measuring $10\text{ cm} \times 6\text{ cm}$ has the same perimeter as a square. Find the square's area, then find by how much it exceeds the rectangle's area.

1. Rectangle's perimeter: $2(10)+2(6) = 32\text{ cm}$.
2. Square's side: $32 \div 4 = 8\text{ cm}$, so its area is $8^2 = 64\text{ cm}^2$.
3. Rectangle's area: $10 \times 6 = 60\text{ cm}^2$.
4. Difference: $64 - 60 = 4\text{ cm}^2$.

A triangle has sides $3x-5$, $2x-1$ and $x+1$ (in cm), and a perimeter of $31$ cm. Find $x$, then find the length of the shortest side.

1. Sum the sides: $(3x-5)+(2x-1)+(x+1) = 6x - 5$.
2. Set equal to the perimeter: $6x - 5 = 31$.
3. Solve: $6x = 36$, so $x = 6$.
4. Side lengths: $3(6)-5=13$, $2(6)-1=11$, $6+1=7$.

Answer: $x=6$; the shortest side is 7 cm.