What you'll learn
The Geometry & Trigonometry domain (~15% of SAT Math) covers area and volume, lines and angles, triangles, circles, and right-triangle trigonometry. Many formulas are provided on the SAT reference sheet — but knowing them saves time.
Key formulas
- Triangle area = ½ × base × height.
- Circle: area = πr², circumference = 2πr.
- Rectangle/box volume = l × w × h; cylinder volume = πr²h.
- Pythagoras: a² + b² = c² (right triangles).
Angles
- Angles in a triangle sum to 180°; in a quadrilateral, 360°.
- Complementary angles sum to 90°; supplementary to 180°.
- Vertical (opposite) angles are equal.
- Interior angles of an n-sided polygon sum to (n − 2) × 180°.
Triangles
- Pythagorean triples: 3-4-5, 5-12-13, 8-15-17 (and multiples) appear constantly — recognise them to skip calculation.
- Special right triangles: 45-45-90 has sides in ratio 1 : 1 : √2; 30-60-90 has ratio 1 : √3 : 2.
- Similar triangles have equal angles and proportional sides. Area scales with the square of the side ratio.
Circles
- An arc and its sector are a fraction of the whole: (central angle ÷ 360°).
- The angle in a semicircle (subtended by a diameter) is 90°.
Right-triangle trigonometry
SOH-CAH-TOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. If sin θ = 3/5, you're looking at a 3-4-5 triangle, so cos θ = 4/5.
Exam strategy
- Sketch the figure if one isn't given.
- Look for hidden right triangles and known triples.
- Use the reference sheet, but recall special-triangle ratios for speed.
Common mistakes
- Mixing up radius and diameter.
- Forgetting area scales with the square of the scale factor.
- Using degrees where radians are intended (and vice versa).
A little memorisation (triples and special triangles) makes this domain fast and reliable.