"Wisconsin Mathematics Formula Reference Sheet"

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Wisconsin Mathematics Formula Reference Sheet
Shape
Formulas for Area (A) and Circumference (C )
1
1
Triangle
A
bh
base
height
2
2
Rectangle
A
lw
length
width
1
1
+ b
Trapezoid
A
(b
)h
sum of bases
height
1
2
2
2
Parallelogram
A
bh
base
height
πr
π
S
2
A
square of radius
Circle
π
C
2πr
2
radius
Figure
Formulas for Volume (V ) and Surface Area (SA)
Rectangular Prism
S
V
lwh
length
width
height
SA
2lw
2hw
2lh
2(length
width)
2(height
width)
2(length
height)
General
S
V
Bh
area of base
height
Prisms
SA
sum of the areas of the faces
Right Circular
S
V
Bh
area of base
height
Cylinder
SA
2B
Ch
(2
area of base)
(circumference
height)
1
1
Right Pyramid
S
V
Bh
area of base
height
3
3
1
SA
B
Pl
2
1
area of base
(
perimeter of base
slant height)
2
Right Circular
1
1
S
V
Bh
area of base
height
Cone
3
3
1
1
SA
B
Cl
area of base
(
circumference
slant height)
2
2
4
4
Sphere
πr
π
S
3
V
cube of radius
3
3
π
2
SA
4πr
4
square of radius
42962
Wisconsin Mathematics Formula Reference Sheet
Shape
Formulas for Area (A) and Circumference (C )
1
1
Triangle
A
bh
base
height
2
2
Rectangle
A
lw
length
width
1
1
+ b
Trapezoid
A
(b
)h
sum of bases
height
1
2
2
2
Parallelogram
A
bh
base
height
πr
π
S
2
A
square of radius
Circle
π
C
2πr
2
radius
Figure
Formulas for Volume (V ) and Surface Area (SA)
Rectangular Prism
S
V
lwh
length
width
height
SA
2lw
2hw
2lh
2(length
width)
2(height
width)
2(length
height)
General
S
V
Bh
area of base
height
Prisms
SA
sum of the areas of the faces
Right Circular
S
V
Bh
area of base
height
Cylinder
SA
2B
Ch
(2
area of base)
(circumference
height)
1
1
Right Pyramid
S
V
Bh
area of base
height
3
3
1
SA
B
Pl
2
1
area of base
(
perimeter of base
slant height)
2
Right Circular
1
1
S
V
Bh
area of base
height
Cone
3
3
1
1
SA
B
Cl
area of base
(
circumference
slant height)
2
2
4
4
Sphere
πr
π
S
3
V
cube of radius
3
3
π
2
SA
4πr
4
square of radius
42962
Equations of a Line
Coordinate Geometry Formulas
Let (x
, y
) and (x
, y
) be two points
1
1
2
2
in the plane.
Slope-Intercept Form:
y
mx
b
y
y
where m
slope and b
y-intercept
2
1
slope
where x
x
x
x
2
1
2
1
y
y
x
x
1
2
1
2
,
midpoint
2
2
Point-Slope Form:
y
y
m(x
x
)
1
1
(
)
2
(
)
2
where m
slope, (x
, y
)
point on line
distance
x
x
y
y
1
1
2
1
2
1
Polygon Angle Formulas
Combinations and Permutations
Sum of degree measures of the interior
angles of a polygon:
180(n
2)
n!
n!
nPr
nCr
r!(n r)!
(n r)!
Degree measure of an interior angle of
a regular polygon:
(
)
180
n
2
n
Formulas for Right Triangles
where n is the number of sides of the polygon
opp
a
Interest Formulas
sin x
c
hyp
c
a
Simple Interest: A
P(1
rt)
adj
b
cos x
x
nt
c
(
)
r
hyp
1
Compound Interest: A
P
n
b
opp
a
A
amount (including interest)
tan x
b
adj
P
principal
r
interest rate (expressed as a decimal)
2
2
2
Pythagorean Theorem: a
b
c
n
number of compoundings per year
t
number of years
Special Right Triangles
Quadratic Equations
2
Let ax
+ bx + c = 0, where a
0.
2
b ±
b
4ac
x
Then
2a
30˚
45˚
b
x-coordinate of vertex =
2
3
2a
2
1
Distance Traveled
45˚
60˚
d
rt
1
1
distance
rate
time
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