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The maximum area of the convex polyon fo...

The maximum area of the convex polyon formed by joining the points `A(0,0),B(2t^2,0),C(18,2),D((8)/(r^2),4)` and `E(0,2)` where `tinR-{0}` and interior angle at vertex B is greater than or equal to `90^@` is

Text Solution

Verified by Experts

The correct Answer is:
54

Slope of `BC =(2-0)/(18-2t^2)ge0`
`rArr18-2t^2ge0`
`rArrt^2-9le0rArrtin[-3,3]`
Now, area of quadrilateral
=Area of trapezium `ABCE+`Area of triangle `CDE `
` (1)/(2) (2t^2+18)xx2+(1)/(2)xx18xx2`
`36+2t^2 le 54`
So, the required maximum area is 54 sq.units.
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