about to only mathematics

Explanation

Equation of tangents at (1, 7) and (4, -2) are

`x+7y - (x+1)-2(y+7)-20=0`
`rArr 5y = 35 rArr y = 7`
and ` 4x - 2y-(x+4)-2(y-2)-20=0`
`rArr 3x - 4y = 20`
`therefore` Point C is (16, 7).
`therefore` Vertices of a quadrilateral are
`A(1, 2)B(1,7),C(16,7), D(4, -2)`
`therefore` Area of quadrilateral ABCD
`= " Area of "DeltaABC+ "Area of "DeltaACD`
`=(1)/(2)xx15xx5+(1)/(2)xx15xx5=75` sq units.