Section 7   Formulas for Area, Volume and Centroid of
Common Geometric Shapes

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Two-dimensional shapes

ShapeAreaPerimeter/Circumference
Rectangle A = l × w    P = 2l + 2w
Circle A = Π × r2   C = 2 × Π × r
Ellipse (where a is the semimajor axis and b is the semiminor axis) A = Π × a × b
  P  =

(a2 + b2) / 2

Triangle A = ½ × b × h P = sum of all sides
Parallelogram b = base, h = height, a = side A = b × h  P = 2a + 2b
Trapezoid (where a and b are the bases)
A =   (  a + b 

  2 
)h
P = sum of all sides

 

Three-dimensional shapes

ShapeVolumeSurface area
Cube V = s3   6s2
Rectangular Prism l = length, h = height, w = width    V = l × w × h   S = 2lw + 2lh + 2wh
Sphere V = (4/3) Πr3   4Πr2
Right Circular Cylinder V = Π × r2 × h   S = 2Π rh + 2Πr2

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