Question 79
Let $a$, $b$, $c$ and $d$ be positive real numbers such that $a^2 + b^2 = c^2 + d^2$.
Determine the largest possible area of a quadrilateral $ABCD$ with side-lengths $|AB| = a$, $|BC| = b$, $|CD| = c$, $|DA| = d$.
Supplemental illustration (AI-generated):
Determine the largest possible area of a quadrilateral $ABCD$ with side-lengths $|AB| = a$, $|BC| = b$, $|CD| = c$, $|DA| = d$.
Supplemental illustration (AI-generated):