Shape Areas

Triangle area using height and base
S = 1/2 ah

Triangle area using two sides and the angle between them
S = 1/2 ab sin(C)

Tringle area using three sides (Heron's formula)
S =saknis(p(p-a)(p-b)(p-c))

Triangle area using semiperimeter and inradius
S = p r

Triangle area using three sides and circumradius
S = a b c / (4 R)

Right triangle area
S = 1/2 ab

Equilateral triangle area
S = a^2 saknis(3) / 4

Area of a square
S = a^2

Area of a square using diagonal
S = 1/2 d^2

Area of a rectangle
S = ab

Area of a rectangle using diagonal
S = 1/2 d^2 sin(φ)

Area of a parallelogram
S = ah

Area of a parallelogram using two sides
S = ab sin(α)

Area of a parallelogram using diagonals
S = 1/2 d1 * d2 sin(φ)

Area of a rhombus
S = a^2 sin(α)

Area of a rhombus using diagonals
S = d1 * d2 / 2

Area of a cyclic quadrilateral
S = saknis((p-a)(p-b)(p-c)(p-d))

Area of a trapezium (trapezoid)
S = (a+b) h / 2

Area of a trapezium (trapezoid) using midline
S = mh

Area of a regular polygon inside circumcircle
S = 1/2 R^2 n sin(360 / n)

Area of a regular polygon
S = n a r / 2

Area of an equilateral triangle using circumradius
S = 3 saknis(3) R^2 / 4

Area of an equilateral triangle using inradius
S = 3 saknis(3) r^2

Area of an equilateral triangle using height
S =saknis(3) h^2 / 3

Area of a square using circumradius
S = 2 R^2

Area of a square using inradius
S = 4 r^2

Area of a regular hexagon
S = 3 saknis(3) a^2 / 2

Area of a regular hexagon using circumradius
S = 3 saknis(3) R^2 / 2

Area of a regular hexagon using inradius
S = 2 saknis(3) r^2

Area of a circle
S = π * R^2

Area of sector of a circle
S = R l / 2

Area of sector of a circle using angle
S = π * R^2 * α / 360

Area of a smaller segment of a circle
S = π * R^2 * α / 360 - S_ΔAOB

Area of a bigger segment of a circle
S = π * R^2 * α / 360 + S_ΔAOB

Area of a segment of a circle
S =  R^2 /2 (π α / 180 - sin(α))