GEOMETRIC FORMULAS

CIRCLE

Area =  Square of Diameter x .7854 or Square of Radius x 3.1416
Circumference = Diameter x 3.1416
Diameter = Circumference x .3183
Doubling diameter increases area four times; tripling diameter increases area nine times, etc.
(Doubling the diameter of a Pipe increases its capacity four times.)

CONE

Area of Curved Surface = Diameter of Base x Slant Height x 1.5708
Volume = Diameter of Base Squared x Perpendicular Height x .2618
or Area of Base x 1/3 Perpendicular Height

CUBE

Area of Surface = Square of Side x 6
Volume = Cube of Side
Diagonal = Side x 1.732

CYLINDER

Area of Curved Surface = Diameter x Length x 3.1416
Volume = Square of Diameter x Length x .7854

HEXAGON (Equal sides and angles)

Area =     Square of Distance across Flats x .866 or Square of Side x 2.598
Side =     1/2 of Diagonal
or Distance across Flats x .577
Diagonal =     Distance across Flats x 1.155 or Side x 2

OCTAGON (Equal sides and angles)

Area = Square of Distance across Flats x .866
Side =     1/2 of Diagonal or Square of Side x 2.598
Diagonal =     Distance across Flats x 1.155 or Side x 2

PARALLELOGRAM

Area = Base x Altitude

PYRAMID

Lateral Surface Area (Not incl. base) = Perimeter of Base x 1/2 of Slant Height
Volume = Area of Base x 1/3 Perpendicular Height

RECTANGLE

Area = Length x Width
Diagonal = Square root of sum of squares of Width and Length

SPHERE

Area of Surface = Square of Diameter x 3.1416
Volume = Cube of Diameter x .5236

SQUARE

Area = Square of Side
Diagonal = Side x 1.4142
Side = Diagonal x .7071

SQUARE INSCRIBED IN CIRCLE

Side of Square = Diameter of Circle x .7071 or Circumference of Circle x .2251
Diameter of Circle = Side of Square x 1.4142

SQUARE AND CIRCLE WITH EQUAL AREA (Circumscribed Circle)

Side of Square = Diameter of Circle x .7071 or Circumference of Circle x .2251
Diameter of Circle = Side of Square x 1.4142
Circumference of Circle = Side of Square x 4.4429

TRIANGLE

Area = Base x 1/2 of Perpendicular Height