I know that there is :FindPartsInRegion3(), but this is more specific. Here is a poorly illustrated example of what I mean.
Figures 2 and 3 would both be in the array. Is there an easy way to figure out if the part is in a state like in Figure 3 and not like Figure 2?
Thanks in advance 
The only way off the top of my head would be to just put another Region3 next to it and see if it’s in that region. But that can be really tolling on a server. You will probably have to do some math with the center point and the corners and determine if they’re all within the bounds. If it’s grid based, i.e. the part will always be going straight into a face of the region, that’s easier because all you have to do is determine if the part’s lower position bounds (position - size/2) is greater than the region’s lower bounds and the upper bounds are lower than the region’s upper bounds.
Thanks for the tips! 
workspace.corner1.Parent = game.ReplicatedStorage
workspace.corner2.Parent = game.ReplicatedStorage
local Point1 = game.ReplicatedStorage.corner1.Position
local Point2 = game.ReplicatedStorage.corner2.Position
local Region = Region3.new(Point1,Point2)
for _,v in next, game.Workspace:FindPartsInRegion3(Region,nil,math.huge) do
print(v.Name)
if (v.Position.X-(v.Size.X/2)) >= Point1.X and (v.Position.X+(v.Size.X/2)) <= Point2.X and (v.Position.Z-(v.Size.Z/2)) >= Point1.Z and (v.Position.Z+(v.Size.Z/2)) <= Point2.Z and (v.Position.Y-(v.Size.Y/2)) >= Point1.Y and (v.Position.Y+(v.Size.Y/2)) <= Point2.Y then
print("yes")
end
end
The corner1 and corner2 just served as a representation for me, can replace them with any Vector3 Positions and does exactly what you want judging by your illustrated example 
Edit:
I modified the code a bit as I forgot to include Y axis checking; as others have mentioned, this doesn’t properly support part rotation.
Thanks for the help! Much appreciated
Doesn’t look like it supports part rotation to me, and is 2D. What about my adjustment below? Sorry if it doesn’t work, I can’t run ROBLOX on my work computer so I gotta hope I didn’t message up 
local gMaxX = Math.max(Point1.X, Point2.X) -- X
local gMinX = Math.min(Point1.X, Point2.X)
local gMaxY = Math.max(Point1.Y, Point2.Y) -- Y
local gMinY = Math.min(Point1.Y, Point2.Y)
local gMaxZ = Math.max(Point1.Z, Point2.Z) -- Z
local gMinZ = Math.min(Point1.Z, Point2.Z)
-- ... for blah in blah do
-- Find all corners of the part
local c1 = v.CFrame * CFrame.new(v.Size.X / 2, v.Size.Y / 2, v.Size.Z / 2)
local c2 = v.CFrame * CFrame.new(-v.Size.X / 2, v.Size.Y / 2, v.Size.Z / 2)
local c3 = v.CFrame * CFrame.new(-v.Size.X / 2, -v.Size.Y / 2, v.Size.Z / 2)
local c4 = v.CFrame * CFrame.new(-v.Size.X / 2, -v.Size.Y / 2, -v.Size.Z / 2)
local c5 = v.CFrame * CFrame.new(v.Size.X / 2, -v.Size.Y / 2, -v.Size.Z / 2)
local c6 = v.CFrame * CFrame.new(v.Size.X / 2, v.Size.Y / 2, -v.Size.Z / 2)
local c7 = v.CFrame * CFrame.new(v.Size.X / 2, -v.Size.Y / 2, v.Size.Z / 2)
local c8 = v.CFrame * CFrame.new(-v.Size.X / 2, v.Size.Y / 2, -v.Size.Z / 2)
-- Find bounds of the part from the corners
local maxX = Math.max(c1.X, c2.X, c3.X, c4.X, c5.X, c6.X, c7.X, c8.X)
local minX = Math.min(c1.X, c2.X, c3.X, c4.X, c5.X, c6.X, c7.X, c8.X)
local maxY = Math.max(c1.Y, c2.Y, c3.Y, c4.Y, c5.Y, c6.Y, c7.Y, c8.Y)
local minY = Math.min(c1.Y, c2.Y, c3.Y, c4.Y, c5.Y, c6.Y, c7.Y, c8.Y)
local maxZ = Math.max(c1.Z, c2.Z, c3.Z, c4.Z, c5.Z, c6.Z, c7.Z, c8.Z)
local minZ = Math.min(c1.Z, c2.Z, c3.Z, c4.Z, c5.Z, c6.Z, c7.Z, c8.Z)
-- Note >= for inclusive. Could change to > for within. Same with <=.
if minX >= gMaxX and maxX <= gMaxX and minY >= gMaxY and maxY <= gMaxY and minZ >= gMaxZ and maxZ <= gMaxZ then
print("yes")
Mine is going to be pretty slow as you add more parts because of all the CFrame operations. I’d grab a pen and paper and math it out if you want it to be quicker.
I second this, using the corners of the part is an effective method of doing this.
It doesn’t.