Some equations for computing area and volume.
This is based on same units of measure for length, width, height, ...
Area is units of measure squared, volume is units of measure cubed.

area rectangle = length times width   length*width
area circle    = Pi * radius * radius
area of triangle = 1/2 * length of side * distance from side to third point
area of triangle given 3 points x1,y1 x2,y2 x3,y3 =
  (x1*y2 - x2*y1 + x2*y3 - x3*y2 + x3*y1 - x1*y3)/2.0
area of ellipse = Pi * a * b  where a = distance center to edge major axis
                                    b = distamce center to edge minor axis
                                    axis perpendicular

For volume, depth is third dimension perpendicular to plane of area
volume = any area * depth
volume cube = length * width * depth
volume sphere = 4/3 * Pi * radius * radius * radius = 4/3 Pi radius^3
volume = any plane area to a point at distance depth = 1/3 area * depth
volume pyramid = 1/3 * length * width * depth
volume cone    = 1/3 * Pi * radius * radius * depth
volume ellipsoid = 4/3 * Pi * a * b * c