Geometric Formulas
Rectangle of Length b and Width a
Area:  

a b

 

Perimeter:  

2 a  +  2 b

 

Parallelogram of Altitude h and Base b
Area:

b h

 

a b   sin Θ

Perimeter:  

2 a  +  2 b

 

Triangle of Altitude h and Base b
Area:

b h

 

a b   sin Θ

Perimeter:  

a + b + c

 

Trapezoid of altitude h and parallel sides a and b
Area:

 

h (a + b)

 

Perimeter:

                   1             1

a + b + h   (  sin Θ  sin Θ  )

 

Regular polygon of n sides each of length b
Area:

 

n b2 cot pi/n

 

Perimeter:  

n b

 

Circle of radius r
Area:

 

pi r2

 

Perimeter:  

2 pi r

 

Sector of circle of radius r
Area:

 

r2 Θ   [Θ in radians]

 

Perimeter:

 

s = r  Θ

 

Radius of circle inscribed in a triangle of sides a,b,c
Area:

           

r = √ s ( s - a ) ( s - b ) ( s - c )

                             s                       

 

where s=(a+b+c) = semiperimeter

 

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=(a+b+c) = semiperimeter

 

Regular polygon of n sides inscribed in circle of radius r
Area:

                       2 pi

n r2   sin     n    

 

Perimeter:

                   pi

2 n r   sin   n   

 

Regular polygon of n sides circumscribing a circle of radius r
Area:

   

                   pi

n r2   tan   n    

 

Perimeter:

 

                  pi

2 n r   tan   n     

 

Segment of circle of radius r

Area:

(shaded part)

 

 

r2 (Θ - sin Θ )

 

 

Ellipse of semi-major axis a and semi-minor axis b
Area:

 

pi a b

 

Perimeter:  

2 pi √ ( a2 + b2 )

 

Rectangular parallelepiped of length a, height b, width c
Volume:

 

a b c

 

Surface area:

 

2 ( ab + ac + bc

 

Right circular cylinder of radius r and height h
Volume:

 

pi r2 h

 

Surface area:  

2 pi r h

 

Right circular cone of radius r and height h
Volume:

 

pi r2 h

           3           

 

Surface area:  

pi r r2 + h2   =   pi r l

 

Pyramid of base area A and height h
Volume:

 

A h

      3       

 

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

 

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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