{
 "source": "https://peabody.kids/flashcards/math-geometry-formulas",
 "id": "math-geometry-formulas",
 "title": "Geometry Formulas: Area, Perimeter, Volume",
 "category": "math",
 "subject": "Math",
 "levels": [
  "6-8",
  "9-12"
 ],
 "description": "The area, perimeter, circumference, surface area and volume formulas every student needs.",
 "tags": [
  "formulas",
  "area",
  "volume",
  "geometry"
 ],
 "frontLabel": "Formula for",
 "backLabel": "Formula",
 "cards": [
  [
   "Area of a rectangle",
   "A = l × w"
  ],
  [
   "Perimeter of a rectangle",
   "P = 2l + 2w"
  ],
  [
   "Area of a square",
   "A = s²"
  ],
  [
   "Perimeter of a square",
   "P = 4s"
  ],
  [
   "Area of a triangle",
   "A = ½ × b × h"
  ],
  [
   "Perimeter of a triangle",
   "Add the three sides"
  ],
  [
   "Area of a parallelogram",
   "A = b × h"
  ],
  [
   "Area of a trapezoid",
   "A = ½ × (b₁ + b₂) × h"
  ],
  [
   "Area of a rhombus",
   "A = ½ × d₁ × d₂",
   "The two diagonals"
  ],
  [
   "Area of a kite",
   "A = ½ × d₁ × d₂"
  ],
  [
   "Area of a circle",
   "A = πr²"
  ],
  [
   "Circumference of a circle",
   "C = 2πr = πd"
  ],
  [
   "Diameter in terms of radius",
   "d = 2r"
  ],
  [
   "Length of an arc",
   "(θ/360) × 2πr, with θ in degrees"
  ],
  [
   "Area of a sector",
   "(θ/360) × πr², with θ in degrees"
  ],
  [
   "Area of an equilateral triangle",
   "A = (√3/4) × s²"
  ],
  [
   "Area of a regular polygon",
   "A = ½ × apothem × perimeter"
  ],
  [
   "Heron's formula",
   "A = √[s(s−a)(s−b)(s−c)], where s is half the perimeter"
  ],
  [
   "Area of a triangle with two sides and the included angle",
   "A = ½ ab sin C"
  ],
  [
   "Area of an ellipse",
   "A = πab",
   "a and b are the semi-axes"
  ],
  [
   "Volume of a cube",
   "V = s³"
  ],
  [
   "Surface area of a cube",
   "SA = 6s²"
  ],
  [
   "Volume of a rectangular prism",
   "V = l × w × h"
  ],
  [
   "Surface area of a rectangular prism",
   "SA = 2(lw + lh + wh)"
  ],
  [
   "Volume of any prism",
   "V = base area × height"
  ],
  [
   "Volume of a cylinder",
   "V = πr²h"
  ],
  [
   "Lateral surface area of a cylinder",
   "2πrh"
  ],
  [
   "Total surface area of a cylinder",
   "SA = 2πr² + 2πrh"
  ],
  [
   "Volume of a cone",
   "V = ⅓πr²h"
  ],
  [
   "Lateral surface area of a cone",
   "πrl, where l is the slant height"
  ],
  [
   "Total surface area of a cone",
   "SA = πr² + πrl"
  ],
  [
   "Volume of a pyramid",
   "V = ⅓ × base area × height"
  ],
  [
   "Volume of a sphere",
   "V = 4/3 πr³"
  ],
  [
   "Surface area of a sphere",
   "SA = 4πr²"
  ],
  [
   "Volume of a hemisphere",
   "V = 2/3 πr³"
  ],
  [
   "Slant height of a cone",
   "l = √(r² + h²)"
  ],
  [
   "Diagonal of a rectangle",
   "d = √(l² + w²)"
  ],
  [
   "Diagonal of a square",
   "d = s√2"
  ],
  [
   "Space diagonal of a rectangular prism",
   "d = √(l² + w² + h²)"
  ],
  [
   "Pythagorean theorem",
   "a² + b² = c²"
  ],
  [
   "Distance formula",
   "d = √[(x₂−x₁)² + (y₂−y₁)²]"
  ],
  [
   "Midpoint formula",
   "((x₁+x₂)/2, (y₁+y₂)/2)"
  ],
  [
   "Slope formula",
   "m = (y₂−y₁)/(x₂−x₁)"
  ],
  [
   "Sum of interior angles of an n-gon",
   "(n − 2) × 180°"
  ],
  [
   "Each interior angle of a regular n-gon",
   "(n − 2) × 180° / n"
  ],
  [
   "Sum of exterior angles of any polygon",
   "360°"
  ],
  [
   "Number of diagonals of an n-gon",
   "n(n − 3)/2"
  ],
  [
   "Equation of a circle",
   "(x − h)² + (y − k)² = r²"
  ],
  [
   "Surface area of a triangular prism",
   "2 × base area + perimeter of base × height"
  ],
  [
   "Volume of a torus",
   "V = 2π²Rr²"
  ],
  [
   "Perimeter of an equilateral triangle",
   "P = 3s"
  ],
  [
   "Area of an annulus (ring)",
   "A = π(R² − r²)"
  ],
  [
   "Area scale factor",
   "If lengths scale by k, area scales by k²"
  ],
  [
   "Volume scale factor",
   "If lengths scale by k, volume scales by k³"
  ]
 ]
}