Question

Suppose a metal worker shapes a 3.4 mg piece of gold until it is a thin, perfectly square plate that is uniformly 8.6x10^-6 cm thick. What is the length of a side of the plate, in cm?

Answer 1

mass = 3.4 mg = 0.0034 grams.
volume Au = mass/density. You will need to look up the density of Au.
Then volume = length x width x thickness. You are given the thickness, you've calculated the volume, left is length and width but since that is a square, you solve for that.
That is volume = side x side x thickness. Solve for side.