Area of Polygons

Area Formulas

Rectangle

$A = l \times w$

Parallelogram

$A = b \times h$ where $b$ = base and $h$ = perpendicular height (not the slant side!)

Triangle

$A = \frac{1}{2} \times b \times h$ A triangle is half of a parallelogram.

Trapezoid

$A = \frac{1}{2}(b_1 + b_2) \times h$ where $b_1$ and $b_2$ are the two parallel bases.

Composite Shapes

Break complex shapes into rectangles, triangles, etc. Find each area, then add (or subtract).

Example: An L-shaped room can be split into two rectangles.

Rectangle 1: $8 \times 5 = 40$ sq ft Rectangle 2: $6 \times 3 = 18$ sq ft Total area: $40 + 18 = 58$ sq ft

Area on the Coordinate Plane

Plot the vertices on a coordinate plane, then use the appropriate formula or count grid squares.

Units

Area is always in square units: $\text{cm}^2$, $\text{ft}^2$, $\text{m}^2$, etc.

Common mistake: For parallelograms and triangles, use the height (perpendicular to the base), not the slant side!