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
with side of
length a
Area =
a2
Perimeter = 4
a
with sides of length
a and
width b:
Area =
ab
Perimeter = 2
a + 2
b
with
height h and
base b and side
a:
_________ ___
/ / |
/ / a h
/____b___/ _|_
th = acute angle between a and b
Area =
bh =
absin(
th)
Perimeter = 2
a + 2
b
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
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))
with
n sides of length
b
Area = 0.25
nb2 cot(
pi/
n)
Perimeter =
nb
with
radius r
Area = pi
r2
Perimeter (
Circumference) = 2 pi
r
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
with height
a and width of base
b
Area = (2/3)
ab
Three Dimensional Objects
with side lengths
a, b, c
Volume =
abc
Surface Area = 2 (
ab +
bc +
ac)
tilted to angle
th
Volume =
abc sin(
th)
with radius
r
Volume = (4/3) pi
r3
Surface Area = 4 pi
r2
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)
With base area =
A and height
h
Volume = (1/3)
Ah
with inner radius
a and outer radius
b
Volume = 0.25 pi
2 (
a +
b) (
b -
a)
2
Surface Area = pi
2 (
b2 -
a2)
with semi-axes
a, b, c
Volume = (4/3)
abc
with height
a and base radius
b
Volume = 0.5 pi
b2a
Analytic Geometry
the
distance d between two points in space - P
1(a,b,c) and P
2(x,y,z)
d = ( (x-a)
2 + (y-b)
2 + (z-c)
2)
1/2
P
1(
x1,
y1) and P
2(
x2,
y2)
y2 - y1
slope = _______
x2 - x1