Let \( \triangle ABC \) be a triangle with \( \angle A = 90^\circ \). The bisectors of angles \( B \) and \( C \) intersect at point \( I \). Suppose that \( IH \) is perpendicular to \( BC \) and \( H \) lies on \( BC \). If \( HB = 5 \text{ cm} \) and \( HC = 8 \text{ cm} \), compute the area of \( \triangle ABC \).

Let's think step by step and output the final answer within \boxed{}.
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