General Formulas

General Formulas

Distance Formula: ((x₂ - x₁)² + (y₂ - y₁)²) where (x₁, y₁) and (x₂, y₂) are points.
Distance Formula in Space: ((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²) where (x₁, y₁, z₁) and (x₂, y₂, z₂) are points.
Midpoint Formula:((A + C)/2), (B + D)/2)) where (A, B) and (C, D) are the endpoints of the segment.
Midpoint Formula in Space:(((A + D)/2), ((B + E)/2), ((C + F)/2)) where (A, B, C) and (D, E, F) are the endpoints of the segment.

Perimeter Formulas

Equilateral Polygon Perimeter Formula: n * s, where n is the number of sides and s is the length of those sides.
Circle Circumference Formula: d where d is the diameter of the circle.

Area Formulas

Triangle Area Formulas: 1/2 * ab * sin(c) where a and b are sides and c is the enclosed angle; 1/2 * hb where h is the height and b is the length of the base.
Equilateral Triangle Area Formulas: (s² * 3) / 4 where s is the length of one side.
Right Triangle Area Formula: Half of the product of the length of the legs.
SSS Triangle Area Formula: the square root of (S(S - a)(S - b)(S - c)) where a, b, and c are sides and S is (a + b + c)/2
Trapezoid Area Formula: 1/2 * h(l₁ + l₂) where h is the altitude and l₁ + l₂ are the bases.
Parallelogram Area Formula: lh where l is the l is the length of one of the bases and h is the length of the altitude.
Circle Area Formula: r² where r is the radius
Pick's Formula: 1/2 * P + I - 1 where P is the number of points on the polygon and I is the number of points in the polygon if the polygon is in a coordinate plane.
Right Prism - Cylinder Lateral Area Formula: ph where the p is the perimeter (circumference) and h is the height
Prism - Cylinder Surface Area Formula: L.A. + 2B where L.A. is the lateral area and B is the area of the base.
Regular Pyramid - Right Cone Lateral Area Formula: 1/2 * lp where l is the length of the slant height and p is the perimeter of the base.
Pyramid - Cone Surface Area Formula: the lateral area plus the area of the base.
Sphere Surface Area Formula: 4r² where r is the radius.

Volume Formulas

Cube Volume Formula: s³ where s is the length of an edge.
Prism - Cylinder Volume Formula: Bh where B is the area of the base and h is the height.
Pyramid - Cone Volume Formula: 1/3 * Bh where B is the area of the base and h is the height.
Sphere Volume Formula: 4/3 * r³ where r is the radius.