Let $ABCD$ be an inscribed trapezoid such that the sides $[AB]$ and $[CD]$ are parallel. If $m(\widehat{AOD})=60^\circ$ and the altitude of the trapezoid is $10$, what is the area of the trapezoid?

Let $N>1$ be an integer. We are adding all remainders when we divide $N$ by all positive integers less than $N$. If this sum is less than $N$, find all possible values of $N$.

$11$ carriers will carry $270$ kg of melons at one step where each melons weighs at most $7$ kg. Each carrier can carry at most $30$ kg in one step. Show that it is possible to carry all the melons at one step whatever a melon weighs.