Area of Triangles and Quadrilaterals

Triangle

Basic formula: $A = \frac{1}{2}bh$ where $b$ = base, $h$ = height (perpendicular to base)

Heron's Formula (when you know all three sides): $A = \sqrt{s(s-a)(s-b)(s-c)}$ where $s = \frac{a+b+c}{2}$ (semi-perimeter)

Rectangle

$A = lw$ where $l$ = length, $w$ = width

Parallelogram

$A = bh$ where $b$ = base, $h$ = height (perpendicular distance between parallel sides)

Trapezoid

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

Can also write as: $A = \frac{1}{2}h(b_1 + b_2)$ or $A = mh$ where $m$ is the midsegment

Rhombus

Method 1: $A = bh$ (like parallelogram)

Method 2: $A = \frac{1}{2}d_1 d_2$ (using diagonals)

Square

$A = s^2$ where $s$ = side length

Key Strategy

Always identify the base and perpendicular height!