Elegant Algebraic Equations for 3D prisms

Shape                                      Formula

Cube                                        A = 6s²                            Where s is a side length.

Rectangular Prism                  A = 2B + Ph

                                               Where B is the area of the base, P is the perimeter of the base and
                                               h is the height.

                                               A = 2(lw + lh + wh)

                                              Where l is the length, w is the width,
                                              and h is the height.

Pyramid                                  A = 4[(bh)/2] + lw

                                              Where b is the base length, h is the height of the triangle (the slant

                                              height), l is the length of the base, and w is the width of the base.

                                               A = B + ½(Ph)

                                              Where B is the area of the base, P is the perimeter of the base,
                                              and h is the height of the triangle (the slant height).

Isosceles triangular prism             A = 2[(b₁h₁)/2]  + 2[(b₂h₂)/2] + B

                                                      Where b₁ and h₁ is the base and height related to the triangle,

                                                       b₂ and h₂ is the base and height related to the rectangles,

                                                      and B is the area of the base.

Cylinder                                          A = 2πr² + (2πr)h                              

        A = 2πr(r + h)                  

        Where r is the radius of the circle.

Where B is found by finding the area of the base (length x width),

and P is the sum of all sides of the base.