Geometry: Area & Volume

Area: The amount of space inside a 2D shape, measured in square units ($\text{cm}^2$, $\text{m}^2$, $\text{in}^2$).

Think of it as: How many unit squares can fit inside the shape. If a rectangle is 4 units by 3 units, you can fit $4 \times 3 = 12$ unit squares inside it.

Units matter: Always include square units in your answer. A rectangle $5 \text{ cm} \times 3 \text{ cm}$ has area $15 \text{ cm}^2$. Notice the units are squared!

Common area formulas: Rectangle: $A = l \times w$, Triangle: $A = \frac{1}{2}bh$, Parallelogram: $A = bh$, Trapezoid: $A = \frac{1}{2}(b_1 + b_2)h$.

Visual understanding: Imagine covering the shape with 1×1 unit squares. Count how many squares fit (or use the formula for faster calculation).

Area vs. Perimeter: Area measures the inside (2D space), perimeter measures the outside (distance around). A large area can have a small perimeter, and vice versa!