How would you sum a range of cells that alternates (skips every other cell) depending on the value of the cell to its left (the every other cell)'s value being non-zero?

Example:
Sum b1 (if a1 is nonzero), d1 (if c1 is nonzero), and f1 (if e1 is nonzero)

pretty sure there is a sumif function.

i found the sumif but it only seems to favor cells next to eachother with a simple range like A1:A10
remember my range is every other cell, requiring additional formulae

add another variable: h

let h be 1 if (a1>0), else let h be 0.
then multiply b1 by h and sum those values.

i bet you can put these equations then into one formula, if you don't want "h" to be in your excel. (don't know excel's syntax very vell)