Essential Geometry Formulas Every SAT Student Must Know

Geometry questions make up about 15% of the SAT Math section, and having the right formulas memorized can be the difference between a good score and a great one. While some formulas are provided in the test booklet, knowing them by heart saves valuable time and reduces errors.

Formulas Provided on the SAT

The SAT does provide some basic formulas, but relying on them can slow you down:

  • Area of a circle: A = πr²
  • Circumference of a circle: C = 2πr
  • Area of a rectangle: A = lw
  • Area of a triangle: A = ½bh
  • Pythagorean theorem: a² + b² = c²
  • Special right triangles: 30-60-90 and 45-45-90

Additional Formulas You MUST Memorize

Triangle Formulas

  • Area using Heron’s formula: A = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2
  • Area of equilateral triangle: A = (√3/4)s² where s is the side length
  • Triangle inequality: The sum of any two sides must be greater than the third side

Circle Formulas

  • Arc length: s = rθ (where θ is in radians)
  • Sector area: A = ½r²θ (where θ is in radians)
  • Converting degrees to radians: radians = degrees × (π/180)

Coordinate Geometry

  • Distance formula: d = √[(x₂-x₁)² + (y₂-y₁)²]
  • Midpoint formula: M = ((x₁+x₂)/2, (y₁+y₂)/2)
  • Slope formula: m = (y₂-y₁)/(x₂-x₁)
  • Point-slope form: y - y₁ = m(x - x₁)

Volume and Surface Area

  • Volume of a cylinder: V = πr²h
  • Volume of a cone: V = ⅓πr²h
  • Volume of a sphere: V = ⅔πr³
  • Surface area of a cylinder: SA = 2πr² + 2πrh

Memory Tips and Tricks

1. Create Visual Associations

For the area of a triangle (A = ½bh), imagine cutting a rectangle in half diagonally.

2. Use Mnemonics

For distance formula: “D-squared equals X-squared plus Y-squared” sounds like a chant.

3. Practice with Real Numbers

Instead of just memorizing, practice with specific values:

  • If r = 3, then area of circle = 9π
  • If sides are 3, 4, 5, then area of triangle = 6

Common SAT Geometry Question Types

Type 1: Special Right Triangles

30-60-90 triangles: sides are in ratio 1 : √3 : 2 45-45-90 triangles: sides are in ratio 1 : 1 : √2

Type 2: Circle Problems

Often involve finding arc length, sector area, or angles in circles.

Type 3: Coordinate Geometry

Frequently test distance, midpoint, and slope calculations.

Type 4: Volume Problems

Usually involve cylinders, cones, or spheres with real-world contexts.

Practice Problem

A cylinder has a radius of 4 units and a height of 6 units. What is the total surface area?

Solution:

  • Surface area = 2πr² + 2πrh
  • SA = 2π(4)² + 2π(4)(6)
  • SA = 2π(16) + 2π(24)
  • SA = 32π + 48π = 80π square units

Strategy for SAT Geometry Success

  1. Memorize formulas completely - don’t rely on the provided ones
  2. Draw diagrams for every geometry problem
  3. Label everything you know from the problem
  4. Look for special triangles and common angle relationships
  5. Check your units - make sure your answer makes sense

Take Your Geometry Skills to the Next Level

Mastering these formulas is just the beginning. The key is practicing with them until they become second nature, allowing you to focus on problem-solving rather than trying to remember formulas.

Ready to master SAT Geometry with personalized instruction? Schedule your free trial session and let’s work together to boost your math confidence!