[OT]Stupid question about sloped armour

This has been bothering me for awhile.	How does sloped armour gain
me anything?

If I take the same mass of sloped armour and make armour perpendicular
to the ground I gain the same thickness you would gain from the
slope.	Space would remain the same (If I pivot the slope about
the center everything I lose from the bottom reappears on the
top.)

The only thing I can think is maybe you increase your chance
of a "glancing" hit.

Where am I off? I'd think my reasoning would be obvious to
any engineer.

Roger