AREA VOLUME AND SURFACE

(pi = = 3.141592...)

Areas

square = a2

rectangle = ab

parallelogram = bh

trapezoid = h/2 (b1 + b2)

circle = pi r 2

ellipse = pi r1 r2

triangle = (1/2) b h

equilateral triangle = (1/4)(3) a2

triangle given SAS = (1/2) a b sin C

triangle given a,b,c = [s(s-a)(s-b)(s-c)] when s = (a+b+c)/2 (Heron's formula)

regular polygon = (1/2) n sin(360°/n) S2
when n = # of sides and S = length from center to a corner

Volumes

cube = a3

rectangular prism = a b c

irregular prism = b h

cylinder = b h = r2 h

pyramid = (1/3) b h

cone = (1/3) b h = 1/3 r2 h

sphere = (4/3) r3

ellipsoid = (4/3) pi r1 r2 r3

Surface Areas

cube = 6 a2

prism:
(lateral area) = perimeter(b) L
(total area) = perimeter(b) L + 2b

sphere = 4 r2

ALGEBRA FORMULAS

(a+b)2 = a2 + 2ab + b2

(a+b)(c+d) = ac + ad + bc + bd

a2 - b2 = (a+b)(a-b) (Difference of squares)

a3 b3 = (a b)(a2 ab + b2) (Sum and Difference of Cubes)

x 2 + (a+b)x + ab = (x + a)(x + b)

if ax2 + bx + c = 0 then x = ( -b (b2 - 4ac) ) / 2a (Quadratic Formula)

MOTHERBOARD

NERVOUS SYSTEM

ENGINE