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This was a labor of html for me =) BTW - formulas is also a valid plural form according to Merriam-Webster. Please message me if I made any errors which I'm sure I have.

Two Dimensional Objects


Square


with side of length a

Area = a2
Perimeter = 4a


Rectangle


with sides of length a and width b:

Area = ab
Perimeter = 2a + 2b


Parallelogram


with height h and base b and side a:


			_________    ___
		       /        /     |
                      /        / a    h
                     /____b___/      _|_
th = acute angle between a and b
Area = bh = absin(th)
Perimeter = 2a + 2b

Triangle


with sides a, b, c and height h

                                  ___
			/\         |
		       /  \        |
                     a/    \ c     |
                     /      \      h
                    /        \     |
                   /____b_____\   _|_

Area = 0.5 bh = 0.5 ab sin(th) = sqrt(s(s-a)*(s-b)*(s-c))
s = semiperimeter = 0.5 (a + b + c)
Perimeter = a + b + c


Trapezoid


with sides a and b and height h


			______a______       ___
		       /	     \       |
                      /               \      h
                     / th            ph\     |
                    /_________b_________\   _|_


Area = 0.5 h(a+b)
Perimeter = a + b + h( 1/(sin(th)) + 1/(sin(ph))


Regular Polygon


with n sides of length b

Area = 0.25 nb2 cot(pi/n)
Perimeter = nb


Circle


with radius r

Area = pi r2
Perimeter (Circumference) = 2 pi r


Ellipse


with semimajor axis a and semiminor axis b

Area = pi ab
Perimeter = 2 pi (0.5(a2 + b2)) ...approximately

more exactly, it is ...
            0.5 pi
             _
            /
            |
            |  /     a2-b2         \0.5
perimeter = |  | 1 - _____ sin(th) |    dth 
            |  \      a2           /
 	    |
           _/
           0


Segment of a Parabola


with height a and width of base b

Area = (2/3) ab


Three Dimensional Objects



Rectangular Parallelepiped


with side lengths a, b, c

Volume = abc
Surface Area = 2 ( ab + bc + ac)


Other Parallelepiped


tilted to angle th

Volume = abc sin(th)


Sphere


with radius r

Volume = (4/3) pi r3
Surface Area = 4 pi r2

Cylinder


with radius r and height h

Volume = pi r2h
Lateral Surface Area = 2 pi rh


Right Circular Cone


with height h and radius of base r

Volume = (1/3) pi r2h
Lateral Surface Area = pi r(r2 + h2)


Pyramid


With base area = A and height h

Volume = (1/3) Ah


Torus


with inner radius a and outer radius b

Volume = 0.25 pi2 (a + b) (b - a)2
Surface Area = pi2 (b2 - a2)


Ellipsoid


with semi-axes a, b, c

Volume = (4/3) abc


Parabaloid


with height a and base radius b

Volume = 0.5 pi b2a


Analytic Geometry



The Distance Formula


the distance d between two points in space - P1(a,b,c) and P2(x,y,z)

d = ( (x-a)2 + (y-b)2 + (z-c)2)1/2


Slope of a Line joining two Points


P1(x1, y1) and P2(x2, y2)

         y2 - y1
slope =  _______
         x2 - x1

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