Area of the regular hexagon whose diagonal is the join of `(2, 4) and (6,7)` is

Answer

`(75sqrt3)/(8)`sq.unit

Explanation

We have A(2,4)and B(6,7) as end points diaginal of the hexagon. ` therefore AB=5`
Thus length of the line segment joining centre of the hexagon and one of the vertices is `(5/2)`.
`therefore` Area of hexagon `=6xx` Area of equilateral triangle having side length ` (5/2)`
`=6xx(sqrt3)/(4)xx(25)/(4)=(75sqrt3)/(8)`