Calculate Hexagon Area with 28 cm² Rectangle Inside: Geometry Problem

Below is a hexagon that contains a rectangle inside it.

The area of the rectangle is 28 cm².

What is the area of the hexagon?

Since we are given the area of the rectangle, let's first work out the length of the missing side:

$7\times a=28$

We'll now divide both sides by 7 to get:

$a=4$

Since all sides are equal in a hexagon, each side is equal to 4.

Now let's calculate the area of the hexagon:

$\frac{6\times a^2\times\sqrt{3}}{4}$

$\frac{6\times4^2\times\sqrt{3}}{4}$

Finally, we simplify the exponent in the denominator of the fraction to get:

$6\times4\times\sqrt{3}=24\times\sqrt{3}=41.56$