All your questions may be answered above. But if you want the width of the hexagon, across the flats, then here is how you calculate it. Start with one of those six equilateral triangles. It is equilateral, so all three sides are equal to the radius of the circle, which is half it's diameter.

Now, draw a line from the center of the circle/hexagon perpendicular to the side of that equilateral triangle that is a chord of the circle. That line is half the distance across the hexagon's flats. And it bisects the equilateral triangle into two right angle triangles. And the simple formula

a^2 + b^2 = c^2

applies. Assuming that c is the radius and b is half the chord (which is also half the radius), then we want to solve for a.

a^2 = c^2 - b^2

or

a = sqrt ( c^2 - b^2 )

Where b = c/2.

You have a 1.5" circle so r and c = 0.75" so:

a = sqrt ( 0.75^2 - 0.375^2 )

a = 0.6495"

But I used only one of the equilateral triangles so a is the distance from the center of the hex to a flat. It must be multiplied by 2 to get the full distance:

2a = 1.2990"