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
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
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

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