Geometry/Appendix A

This is an incomplete list of formulas used in geometry. Length Perimeter and Circumference Polygon Sum the lengths of the sides. Circle is the diameter is the radius Triangles Law of Sines: are sides, are the angles corresponding to respectively. Law of Cosines: are sides, are the angles corresponding to respectively. Right Triangles Pythagorean Theorem: are sides where c is greater than other two. Area Triangles = base, = height (perpendicular to base), = area Heron's Formula: are sides, and , = area Equilateral Triangles is a side Quadrilaterals Squares is the length of the square's side Rectangles and are the sides of the rectangle Parallelograms is the base, is the height Trapezoids are the two bases, is the height Circles is the radius Surface Areas 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 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 Chapter 21 Appendix B Geometry (book)