# What is the area of this hexagon?

Jan 26, 2016

The are of an octagon is $2 {a}^{2} \left(1 + \sqrt{2}\right)$ where $a$ is the side

to find the side from the height we have that $h = a \left(1 + \sqrt{2}\right)$ so:

$10 = a \left(1 + \sqrt{2}\right)$

$a = \frac{10}{1 + \sqrt{2}}$

plugging that into the equation for the area we have:

$A = 2 \cdot \frac{100}{1 + \sqrt{2}} ^ 2 \cdot \left(1 + \sqrt{2}\right)$

That simplifies to:

$A = \frac{200}{1 + \sqrt{2}} = 82.8427$