1. Perimeter & Area: Edges vs. Surface

Two ideas trip students up because they sound similar but measure very different things.

Perimeter is the distance around a shape — imagine walking along its edge. It is a length, measured in cm, m, ft. For a rectangle, \(P = 2(l + w)\) because there are two lengths and two widths.

Area is the amount of flat surface inside — imagine the tiles needed to cover a floor. It is measured in square units (\(\text{cm}^2\), \(\text{m}^2\)). For a rectangle, \(A = l \times w\).

Example: a room \(8\,\text{m}\) by \(5\,\text{m}\).
\[ P = 2(8+5) = 26\,\text{m}, \qquad A = 8 \times 5 = 40\,\text{m}^2. \]
A triangle's area is \(A = \frac{1}{2} b h\) — a triangle is literally half of a rectangle that surrounds it.

⚠️ Common mistake: mixing up the units. If the answer is a length use single units; if it's a surface use square units.