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Q.
Area of the regular hexagon whose diagonal joins $(2,4)$ and $(6,7)$ is
Straight Lines
Solution:
We have $A(2,4)$ and $B(6,7)$ as end points of diagonal of the hexagon.
$\therefore A B=5$
So, length of the line segment joining centre of the hexagon and one of the vertices is $\frac{5}{2}$.
$\therefore$ Area of hexagon $=6 \times$ Area of equilateral triangle having side length $\frac{5}{2}$
$=6 \times \frac{\sqrt{3}}{4} \times \frac{25}{4} $
$=\frac{75 \sqrt{3}}{8}$