The maximum area of the convex polygon formed by joining the points A(0, 0), B(2t2,0), C(18,2), D8t2,4 and E(0,2), where t∈R−{0} and interior angle at vertex B is greater than or equal to 90° is _______ .

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answer is 54.

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Detailed Solution

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

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