The maximum area of the convex polygon formed by joining the points A0,0, B2t2,0,C18,2, D8r2,4 and E0,2, where t∈R−0 and interior angle at vertex B is greater than or equal to 900 is

Slope of BC=2−018−2t2≥0⇒18−2t2≥0⇒t2−9≤0⇒t∈−3,3Now area of quadrilateral = Area of trapezium ABCE+Area of triangle CDE=122t2+18×2+12×18×2=36+2t2≤54So, the required maximum area is 54 aq. units