Q:

Find total yards with LXWXH?

I have a box I need to cover all 6 sides with a single layer fiberglass fabric. The fabric comes in 50" or 28" widths.  The dimensions of the box are 34" long; 15" wide; 12" High. How do I determine how many total yards I need to buy depending on the the width I choose?

A:

The box is a rectangular prism, so there are three pairs of identical sides. So, we can calculate the surface area of each of the unique sides, sum these, then multiply by $2$.
The first unique side is: $34'' \times 15'' = 510$ square inches.
The second: $34'' \times 12'' = 408$ square inches.
The third: $15'' \times 12'' = 180$ square inches.
Sum these and multiply by $2$, and we have $2196$ square inches.
As for how many of a certain sheet it'll take, that depends on the length of the fabric sheets. We can just generalize and say they're $28 \times x$ and $50 \times x$ square inch sheets. So, they area of a sheet would be $28x$ and $50x$, respectively. To determine how many of either sheet you'd need, you just compute $2196/28x$ and $2196/50x$ for each size of sheet.

