Geometry/Appendix A

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This is an incomplete list of formulas used in geometry.

Length[edit]

Perimeter and Circumference[edit]

Polygon[edit]

  • Sum the lengths of the sides.

Circle[edit]

    • is the diameter
    • is the radius

Triangles[edit]

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

Right Triangles[edit]

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

Area[edit]

Triangles[edit]

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

Equilateral Triangles[edit]

    • is a side

Quadrilaterals[edit]

Squares[edit]

    • is the length of the square's side

Rectangles[edit]

    • and are the sides of the rectangle

Parallelograms[edit]

    • is the base, is the height

Trapezoids[edit]

    • are the two bases, is the height

Circles[edit]

    • is the radius

Surface Areas[edit]

  • 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.

Volume[edit]

  • 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