# Useful Formulas

### VALUES

TRIANGLE: A = ab / 2 (a = height, b = base): half the product of the base height

SQUARE: A = a2 (to one of the sides)

RECTANGLE: A = ab (at height, b base): product of the base height

TRAPECIO: A = a (b + c) / 2 (b longest side, c shortest side, at height): half the product of the height by the sum of the parallel sides

REGULAR PENTAGON: A = 1,720 a2 (to one of the squares)

REGULAR HEXAGON: A = 2,598 a2 (to one of the sides)

REGULAR OCTAGON: A = 4.828 a2 (to one of the sides)

CIRCLE: A = ¶R2 (¶ 3.14159, r radius)

SPHERICAL SURFACE: 4¶ r2, in other words 4 times the area of ??the circle.

PI (¶) is the ratio of the length of a circle to its diameter; its value with 14 decimals is 3.14159265358989; in practice, 3.14159 is used.

CIRCUMFERENCE: C = 2¶ r (¶ 3.14159, r radius) So the length of the circumference is equal to twice the radius (ie the diameter) for the reason ¶

CUBE: V = a3 (to one of the edges)

RECTANGULAR PRISM: V = abc (a length, b width, c depth)

PYRAMID: V = Ah / 3 (A area of ??the base, h height): third part of the product of the area of ??the base

CYLINDER: V = ¶r2h, that is, the area of ??the base (which is a circle) by the height (h)

CONE: V = ¶r2h / 3 a third of the base area by height (h)

SPHERE: V = 4¶r2 = / 3 (¶ 3.14159, radius r)

CONVERSION OF THE MATTER IN ENERGY: E = mc2 (E represents the energy in ergios, m the mass or matter in grams and c the speed of light in centimeters per second, or the figure of 30,000 million).