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      Mr. Manns' Class    

Area and Volume Formulas

 

                                        Area of a rectangle         A = b · h                      or          A = l · w

                                               Area of a square         A = b · h                      or          A = l · w

                                            Area of a rhombus        A = b · h                      or          A = l · w

                             Area of a parallelogram         A = b · h                      or          A = l · w

                                            Area of a triangle         A = ½ · b · h                or          A = ½ · l · w

                                          Area of a Trapezoid         A = ½ · h · (a + b)

                                                 Area of a circle         A = p · r2

 

                                            Perimeter of a Polygon         Sum of the sides

                                   Circumference of a Circle         C = p · d

 

(In the volume formulas below, the capital ‘B’ stands for “the area of the base of the given figure.)

 

                                                Volume of a Cube         V = B · h                      or          V = l · w · h

                 Volume of a Rectangular Prism         V = B · h                      or          V = l · w · h

                     Volume of a Triangular Prism         V = B · h                      or          V = ½ · l · w · h

                    Volume of a Trapezoidal Prism         V = B · h                      or          V = [½· h · (a + b)] · h

                                       Volume of a Cylinder         V = B · h                      or          V = p · r2 · h

 

                        Volume of a Square Pyramid         V = 1/3 · B · h               or          V = 1/3 · l · w · h

           Volume of a Rectangular Pyramid         V = 1/3 · B · h               or          V = 1/3 · l · w · h

               Volume of a Triangular Pyramid         V = 1/3 · B · h               or          V = 1/3 · ½ · l · w · h

                                                Volume of a Cone         V = 1/3 · B · h               or          V = 1/3 · p · r2 · h

                                                Volume of a Sphere         V = 4/3 · p · r3

 

THINGS TO NOTICE

-         Only circles, cones, cylinders, and spheres use pi (p).  Only figures made of or with circles will use p.

-         All formulas that have a triangular part have ½ in it.  (Although they are not the only ones that have ½ in them.)

-         All the formulas for cones and pyramids start with the fraction 1/3.  These are all the figures that come up to a point.

-         Many of the Volume formulas have an alternate formula using a capital ‘B’.  In these formulas, the capital ‘B’ stands for the area of the base of the given figure.

-         In the Area of a Trapezoid formula and the Volume of a Trapezoidal Prism formula the (a + b) represent the two bases of the Trapezoid.  The two parallel sides of a Trapezoid are some times referred to as bases.  The ‘a’ and ‘b’ in that formula are the bases of the Trapezoid.

-         In the Volume of a Trapezoidal Prism formula, there are two ‘h’ values.  The first ‘h’ inside the parenthesis is the height of the Trapezoid.  The ‘h’ outside the parenthesis is the height of the Prism.