Solid figure reached out into river (10)
I believe the answer is:
decahedron
'solid figure' is the definition.
(I've seen this before)
'reached out into river' is the wordplay.
'out' indicates an anagram (out can mean wrong or inaccurate).
'into' indicates putting letters inside.
'river' becomes 'don' (I've seen this before).
'reached' with letters rearranged gives 'ecahedr'.
'ecahedr' going within 'don' is 'DECAHEDRON'.
(Other definitions for decahedron that I've seen before include "Solid figure with ten plane faces" , "Ten-faced solid" , "Ten-faced figure" .)