Area of 2D Shapes

Key Area Formulas

Shape	Formula
Rectangle	$A = lw$
Square	$A = s^2$
Triangle	$A = \frac{1}{2}bh$
Parallelogram	$A = bh$
Trapezoid	$A = \frac{1}{2}(b_1 + b_2)h$
Circle	$A = \pi r^2$

All heights ($h$) must be perpendicular to the base.

Composite Figures

Break complex shapes into simpler parts:

• Add areas of parts that make up the shape.
• Subtract areas of parts that are removed.

Example: An L-shaped room = large rectangle − small rectangle cut from corner.

Shaded Region Problems

A common SAT pattern: find the area of a shaded region by subtracting the unshaded part from the whole.

$A_{\text{shaded}} = A_{\text{outer}} - A_{\text{inner}}$

Example: A circle inscribed in a square. Shaded area = square area − circle area.

If the square has side $s$ and the circle has radius $r = s/2$:

$A_{\text{shaded}} = s^2 - \pi(s/2)^2 = s^2 - \frac{\pi s^2}{4}$

Tip 1: The SAT Provides Formulas

Area formulas for standard shapes are on the SAT reference sheet. But knowing them saves time.

Tip 2: Height Must Be Perpendicular

For triangles and parallelograms, don't use the slant side — use the perpendicular height.

Tip 3: Draw Helper Lines

For composite shapes, draw dashed lines to split the shape into rectangles and triangles.

Tip 4: Label Everything

Write dimensions on the figure to keep track.