Geometry/Appendix A

This is an incomplete list of formulas used in geometry.

LengthEdit

Perimeter and CircumferenceEdit

PolygonEdit

  • Sum the lengths of the sides.

CircleEdit

  •  
    •   is the diameter
    •   is the radius

TrianglesEdit

  • Law of Sines:  
    •   are sides,   are the angles corresponding to   respectively.
  • Law of Cosines:  
    •   are sides,   are the angles corresponding to   respectively.

Right TrianglesEdit

  • Pythagorean Theorem:  
    •   are sides where c is greater than other two.

AreaEdit

TrianglesEdit

  •  
    •   = base,   = height (perpendicular to base),   = area
  • Heron's Formula:  
    •   are sides, and  ,   = area

Equilateral TrianglesEdit

  •  
    •   is a side

QuadrilateralsEdit

SquaresEdit

  •  
    •   is the length of the square's side

RectanglesEdit

  •  
    •   and   are the sides of the rectangle

ParallelogramsEdit

  •  
    •   is the base,   is the height

TrapezoidsEdit

  •  
    •   are the two bases,   is the height

CirclesEdit

  •  
    •   is the radius

Surface AreasEdit

  • Cube: 6×( )
    •   is the length of a side.
  • Rectangular Prism: 2×((  ×  ) + (  ×  ) + (  ×  ))
    •  ,  , and   are the length, width, and height of the prism
  • Sphere: 4×π×( 2)
    •   is the radius of the sphere
  • Cylinder: 2×π× ×(  +  )
    •   is the radius of the circular base, and   is the height
  • Pyramid:  
    •   = Surface area,   = Area of the Base,   = Perimeter of the base,   = slant height.
The surface area of a regular pyramid can also be determined based only on the number of sides( ), the radius( ) or side length( ), and the height( )
If   is known,   is defined as  
or if   is known,   is defined as  
The slant height   is given by  
The total surface area of the pyramid is given by  
  • Cone: π×r×(r + √(r2 + h2))
    •   is the radius of the circular base, and   is the height.

VolumeEdit

  • Cube  
    • s = length of a side
  • Rectangular Prism  
    • l = length, w = width, h = height
  • Cylinder(Circular Prism) 
    • r = radius of circular face, h = distance between faces
  • Any prism that has a constant cross sectional area along the height:
    •  
    • A = area of the base, h = height
  • Sphere:  
    • r = radius of sphere
  • Ellipsoid:  
    • a, b, c = semi-axes of ellipsoid
  • Pyramid:  
    • A = area of base, h = height from base to apex
  • Cone (circular-based pyramid): 
    • r = radius of circle at base, h = distance from base to tip

Navigation

Chapter 21 · Appendix B