IKMC 2027 - Grades 7-8 - Self-study SET 2 - Thematic Batch 3 Question 13

Points $A,B,C,D$ lie on the sides of square $KLMN$ as shown. Point $O$ is its centre. Given $OA\perp OB$, $OC\perp OD$ and $LM=2$, what is the grey area?