Geometric Formulas |
Rectangle of Length b and Width a |
Area: |
a b
|
Perimeter: |
2 a + 2 b
|
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Parallelogram of Altitude h and Base b |
Area: |
b h
a b sin Θ |
Perimeter: |
2 a + 2 b
|
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Triangle of Altitude h and Base b |
Area: |
½ b h
½ a b sin Θ |
Perimeter: |
a + b + c
|
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Trapezoid of altitude h
and parallel sides a and b |
Area: |
½ h (a + b) |
Perimeter: |
1
1
a + b +
h (
sin Θ
+ sin
Θ ) |
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Regular polygon of n
sides each of length b |
Area: |
¼ n b2 cot pi/n |
Perimeter: |
n b
|
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Circle of radius r |
Area: |
pi r2 |
Perimeter: |
2 pi r
|
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Sector of circle of radius r |
Area: |
½ r2 Θ [Θ in
radians] |
Perimeter: |
s = r Θ |
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Radius of circle inscribed in a
triangle of sides a,b,c |
Area: |
r = √
s ( s - a ) ( s - b ) ( s - c )
s
where s=½(a+b+c) = semiperimeter |
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Radius of circle circumscribing
a triangle of sides a,b,c |
Area: |
a b c
R =
4 √ s
( s
- a ) ( s - b ) ( s - c )
where s=½(a+b+c) = semiperimeter |
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Regular polygon of n
sides inscribed in circle of radius r |
Area: |
2 pi ½ n r2
sin
n
|
Perimeter: |
pi 2 n r
sin n
|
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Regular polygon of n sides
circumscribing a circle of radius r |
Area: |
pi n r2
tan n
|
Perimeter: |
pi 2 n r
tan n
|
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Segment of circle of radius r |
Area:
(shaded part) |
½ r2 (Θ - sin Θ )
|
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Ellipse of semi-major axis a
and semi-minor axis b |
Area: |
pi a b |
Perimeter: |
2 pi √ ½ ( a2
+ b2
)
|
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Rectangular parallelepiped of
length a, height b, width c |
Volume: |
a b c |
Surface area: |
2 ( ab + ac + bc )
|
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Right circular cylinder of
radius r and height h |
Volume: |
pi r2 h |
Surface area: |
2 pi r h
|
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Right circular cone of radius
r and height h |
Volume: |
pi r2 h
3
|
Surface area: |
pi r √ r2
+ h2 =
pi r l
|
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Pyramid of base area A
and height h |
Volume: |
A h
3
|
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Frustrum of right circular cone
of radii a, b and height h |
Volume: |
pi h ( a2 + ab + b2
)
3
|
Surface area: |
pi (a + b) √
h2
+ (b - a)2
= pi ( a +
b ) l
|
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Torus of inner radius a
and outer radius b |
Volume: |
pi2 ( a + b ) ( b - a )2
4
|
Surface area: |
pi2 ( b2 - a2 )
|
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