Calculate the Area of an Equilateral Hexagon with Side Length 7 and Height 12.124

Question

Below is an equilateral hexagon.

AB = 7
FC = 14
AE = 12.124

What is the area of the hexagon?

00:12 Let's find the area of this hexagon together!

00:15 We'll use a special formula for the area of a regular hexagon.

00:23 Check the given data for the side length.

00:31 This hexagon is equilateral, meaning all sides are equal.

00:38 Now, let's plug in the side length into our formula and find the area!

00:59 And there you have it! That's how we solve this problem.

The hexagon consists of two equal trapezoids, so we will strive to calculate the area of one of them and multiply it.

AFE is an isosceles triangle,

its height (FG) crosses the base exactly in the center, therefore:

$AG=GE$

$AG=\frac{1}{2}AE$

We replace and discover:

$AE=\frac{1}{2}\times12=6$

We replace the data in the formula for the area of a trapezoid:

$\frac{(base+base)}{2}\times altura$

$\frac{7+14}{2}\times6=\frac{21}{2}\times6=10.5\times6=63$

63 is the area of half of the hexagon, therefore:

$63\times2=126$

127.3