Let Ks1,s2,⋯,sr(r) be the complete r-partite r-uniform hypergraph and ex(n,Ks1,s2,⋯,sr(r)) be the maximum number of edges in any n-vertex Ks1,s2,⋯,sr(r)-free r-uniform hypergraph. It is well-known in the graph case [19,18] that ex(n,Ks,t)=Θ(n2−1/s) when t is sufficiently larger than s. In this note, we generalize the above to hypergraphs by showing that if sr is sufficiently larger than s1,s2,⋯,sr−1 thenex(n,Ks1,s2,⋯,sr(r))=Θ(nr−1s1s2⋯sr−1). This follows from a more general Turán type result we establish in hypergraphs, which also improves and generalizes some recent results of Alon and Shikhelman [2]. The lower bounds of our results are obtained by the powerful random algebraic method of Bukh [6]. Another new, perhaps unsurprising insight which we provide here is that one can also use the random algebraic method to construct non-degenerate (hyper-)graphs for various Turán type problems.The asymptotics for ex(n,Ks1,s2,⋯,sr(r)) is also proved by Verstraëte [25] independently with a different approach.