How to Spawn part in a random area within a perimeter?

For example, if I had a part as a base, how would I make it so that I can spawn smaller parts anywhere within the perimeter of the base?

The position of a part is located in the very center. Relative to the part, this is also known as Size:{X/2, Y/2, Z/2}. To get the amount of space it takes up on a 2D plane, you would simply add and subtract these dimensions from the part's position to get where it starts and where it ends. Remember, the position starts in the middle.

-- Get the Base's position and size
-- This is assuming 'base' is defined
local pos = base.Position
local size = base.Size

-- Get the half-way point of both xz dimensions 
local x_half = size.X/2
local z_half = size.Z/2

-- Get the range of both dimensions
-- This will return where X begins and ends, and where Z begins and ends.
local x_vec = Vector2.new(pos.X - x_half, pos.X + x_half)
local z_vec = Vector2.new(pos.Z - z_half, pos.Z + z_half)

Now you can randomly choose between these ranges to get any point within the base's 2D scale. For example:

-- Let's make the code above into a function
local function get2DScale(part)
	local pos = part.Position
	local size = part.Size

	local x_half = size.X/2
	local z_half = size.Z/2

	local x_vec = Vector2.new(pos.X - x_half, pos.X + x_half)
	local z_vec = Vector2.new(pos.Z - z_half, pos.Z + z_half)

	return x_vec, z_vec
end

-- Assuming 'part' and 'base' is defined
local baseVecX, baseVecY = get2DScale(base)

part.CFrame = CFrame.new(
	math.random(baseVecX.X, baseVecX.Y),
	math.random(x), -- Whatever you want your height to range between
	math.random(baseVecY.X, baseVecY.Y)
)

This would randomly position a part somewhere on that base grid. Hope that helps, if you have any questions, just let me know.