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Formulas: Trigometry and Geometry
NOTE: pi = 3.14159265358979323846
Perimeters/Circumferences (2-D)
Circle: Circumference = pi * diameter
Rectangle: Perimeter = 2 * length + 2 * width
Square: Perimeter = 4 * side
Triangle: Perimeter = 3 * side
Regular Hexagon: Perimeter = 6 * side
Trapezoid: Perimeter = 2 * aside + 2 * bside
Note: aside and bside are measurements of two consecutive sides of the trapezoid.
Diagonals (2-D)
Diamond Square: side = SQR(diag
^{2}/2)
Square: Diagonal = (side
^{2} * 2)
^{1/2} or SQR((side
^{2} * 2))
Circle: Diameter = radius * 2, radius = diameter/2
Rectangle: Diagonal = (length
^{2} * width
^{2})
^{1/2}
Triangle (Perfect): Height = (side * SQR(3))/2
Areas (2-D)
Triangle: Area = (base * height) / 2
Triangle (Perfect): Area = (side/2)
^{2} * SQR(3)
Triangle (Perfect): Area = SQR (side
^{2} - (side/2)
^{2})
Diamond Square: AREA = diagonal
^{2}/2
Square: Area = side
^{2}
Rectangle: Area = length * width
Parallelgram: Area = base * height
Trapezoid: Area = height * (base1 + base2)/2
Wrecktangle: Divide into two triangles and use triangle forula to combine
Circle: Area = pi * radius
^{2}
Ellipse: Area = pi * a * b
Trapezoid: Area = (height*(aside + bside))/2
Note: aside and bside are measurements of two consecutive sides of the trapezoid.
Regular Pentagon: Area = 1.720 * side
^{2}
Regular Hexagon: Area = 2.598 * side
^{2}
Regular Hexagon: Area = 3 * (side/2)
^{2} * SQR(3)
Regular Octagon: Area = 4.828 * side
^{2}
Edge Length (3-D)
Cube: Edge = side * 12
Rectangular Prism: Edge = length * 4 + width * 4 + height * 4
Tetrahedron (4-sided Triangular Figure): Edge = side * 6
Diagonals (3-D)
Cube:
Surface Areas (3-D)
Cube: Area = side
^{2} * 6
Rectangular Prism: Area = 2 * (length * width + width * height + height * length)
Tetrahedron: Area = (base * height) * 2
Sphere: Area = radius
^{2} * pi * 4
Volume (3-D)
Cube: Volume = side
^{3}
Rectangluar Prism: Volume = length * width * height
Pyramid: Volume = (AreaOfBase * height)/3
Cylinder: Volume = pi * r
^{2} * height
Cone: Volume = (pi * r
^{2} * height)/3
Sphere: Volume = (4 * pi * r
^{3})/3
Temperature Conversions
Celsius = (Fahrenheit - 32) / 1.8
Fahrenheit = (Celsius * 1.8) + 32
Absolute Zero = -273.16 degrees Celsius or Zero degrees Kelvin!