Geometry/Appendix A
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< Geometry
This is an incomplete list of formulas used in geometry.
Contents
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.
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 + √(r^{2} + h^{2}))
 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 = semiaxes of ellipsoid
 Pyramid:
 A = area of base, h = height from base to apex
 Cone (circularbased pyramid):
 r = radius of circle at base, h = distance from base to tip
 Geometry Main Page
 Motivation
 Introduction
 Geometry/Chapter 1 Definitions and Reasoning (Introduction)
 Geometry/Chapter 1/Lesson 1 Introduction
 Geometry/Chapter 1/Lesson 2 Reasoning
 Geometry/Chapter 1/Lesson 3 Undefined Terms
 Geometry/Chapter 1/Lesson 4 Axioms/Postulates
 Geometry/Chapter 1/Lesson 5 Theorems
 Geometry/Chapter 1/Vocabulary Vocabulary
 Geometry/Chapter 2 Proofs
 Geometry/Chapter 3 Logical Arguments
 Geometry/Chapter 4 Congruence and Similarity
 Geometry/Chapter 5 Triangle: Congruence and Similiarity
 Geometry/Chapter 6 Triangle: Inequality Theorem
 Geometry/Chapter 7 Parallel Lines, Quadrilaterals, and Circles
 Geometry/Chapter 8 Perimeters, Areas, Volumes
 Geometry/Chapter 9 Prisms, Pyramids, Spheres
 Geometry/Chapter 10 Polygons
 Geometry/Chapter 11
 Geometry/Chapter 12 Angles: Interior and Exterior
 Geometry/Chapter 13 Angles: Complementary, Supplementary, Vertical
 Geometry/Chapter 14 Pythagorean Theorem: Proof
 Geometry/Chapter 15 Pythagorean Theorem: Distance and Triangles
 Geometry/Chapter 16 Constructions
 Geometry/Chapter 17 Coordinate Geometry
 Geometry/Chapter 18 Trigonometry
 Geometry/Chapter 19 Trigonometry: Solving Triangles
 Geometry/Chapter 20 Special Right Triangles
 Geometry/Chapter 21 Chords, Secants, Tangents, Inscribed Angles, Circumscribed Angles
 Geometry/Chapter 22 Rigid Motion
 Geometry/Appendix A Formulas
 Geometry/Appendix B Answers to problems
 Appendix C. Geometry/Postulates & Definitions
 Appendix D. Geometry/The SMSG Postulates for Euclidean Geometry