Question Number 217047 by hardmath last updated on 27/Feb/25
$$\mathrm{Parties}\:-\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d} \\ $$$$\mathrm{For}\:\mathrm{a}\:\mathrm{convex}\:\mathrm{quadrilateral} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{Area}\left(\mathrm{ABCD}\right)\:\leqslant\:\frac{\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \:+\:\mathrm{d}^{\mathrm{2}} }{\mathrm{4}} \\ $$