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Mathematical

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 Plane Figure Formulae

 

 

 

      

 

 

 

 

 

 1.       Given A, B and c, find b, C and c

 

     a sinB                     a sin C

  b= ------ , C=180o-(A+B), c= --------

        A                        sin A

 

 

 2.      Given A, a and b, find B, C and c

 

         b sinA                     a sinC

  sin B= ------ , C=180o-(A+B), c= -------

           a                         sinA

 

 

 3.      Given a, b and c, find A, B and c

 

 

           a sinC                      a sinC

  tan A= ---------- , B=180o-(A+C), c= -------

         b-(a cosC)                     sinA

 

 

 4.      Given a, b and c, find A, B and C

 

         b2+c2-a2          a2+c2-b2

  cos A= -------- , cosB= --------- , C=180o-(A+B)

                              2ac

 

 

 5.      Given a, b, c, A, B and C, find Area

 

 

     a+b+c

  s= ----- , Area=√s(s-a)(s-b)(s-c)

       2

 

         bc sinA          a2 sin B sin C

  Area = ------- , Area = --------------

            2                2 sinA

 

 

  Rectangle

 

 

 

 If square, a=b

 Area = ab

 Perimeter = 2(a+b)

 Diagonal =   ________

            \/a2+b2

 

 

  Parallelogram

 

 

 

 

 All sides are parallel

 z = degrees

 

 Area = ah = ab sin z

 Perimeter = 2(a + b)

 

 

  Trapezoid

 

 

 

 

 Area = (a + b)

        ------- h

           2

 Perimeter = Sum of lengths of sides

 

 

  Quadrilateral

 

 

 z = degrees

 

 

        d1 x d2 s sin z

 Area = ---------------

               2

 

  Trapezium

 

 a to g = lengths

 Perimeter = a + b + c + d

 

        (h+k)g+eh+fk

 Area = ------------

               2

 

 

  Equilateral Triangle

 

 

 

 a = all sides equal

 Perimeter = 3a

 

      a   __

 h =  - \/3  = 0.866 a

      2

             _

           \/3

 Area = a2 ---- = 0.433 a2

             4

 

   Annulus

 

 

 

 Area = .7854(d2-f2)

 

 Area  = pi(r1 + r2)(r2 - r1)

 

 

 

 

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