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Jaloopa

The bottom row are all identical to the baubles underneath.

The two below the 14 are a cube and a triangle that add up to 14.

Only possible values for the cube are 1 and 8
If 1 then the triangle is 13, which isn't a triangle number, so it must be 8 and 6

hungrier

The two on the bottom right are:
A triangle x
A square y
such that 8 + 2x + y = 23

math hard; shopping

3 and 9

This lets you fill in a bunch of them, up to the one above 23.

CarrieVS

Filling in all the above solutions, there's only one number left on the bottom row (left hand square) - call it S_l

This makes it fairly easy to work up to the two higher numbers and the higher square and triangle (S_h and T, respectively).

S_l + 6 + 14 + 25 + S_h 106 <=> S_l + S_h = 61

Similarly (but not forgetting to add 48 twice):
S_l + T = 57

The only pair of square numbers adding to 61 is 25 and 36

If S_l = 25 => T = 32
If S_l = 36 => T = 21
Since 21 is a triangle number and 32 is not, then:
S_l = 36, S_h = 25, and T = 21

This makes the value of the star 433, if all my arithmetic is correct. The intermediate values are left as an exercise for the reader.

xaade

@carrievs That's what I got.