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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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