Let A(2t−1,3), B(4,t2) and C(1,2t+1) be the three vertices of a triangle, where t is a real parameter.
(i) Express the area S(t) of △ABC entirely in terms of t.
(ii) Hence determine all real values of t for which the area of the triangle equals 10 square units.
(iii) For each admissible value of t obtained in part (ii), write down the three vertices explicitly and state whether the triangle is acute‐angled, right‐angled or obtuse‐angled, giving suitable justification based on side lengths.