One of the most amazing things that happens in nature is the ability of bees to make a honeycomb. each cell of the honeycomb is a regular hexagon. if the side of one of these honeycomb cells is 2 millimeters, then what is its area? round your answer to the nearest tenth. use the equation a = ½ap for the area of the regular polygon.

Step-by-step explanation:

Please consider the attached image.

We have been given that each cell of the honeycomb is a regular hexagon. The side of one of these honeycomb cells is 2 millimeters.

We know that a regular hexagon is made of 6 equilateral triangles.

Let us find apothem of our given hexagon using Pythagoras theorem as:

Take positive square root of both sides:

Now, we will use formula for the area of the regular polygon to solve our given problem as:

A = ½ap, where,

A = Area of the regular polygon,

a = Apothem,

p = Perimeter of polygon.

Perimeter of our given hexagon would be 6 times 2 millimeters:

Round to nearest tenth:

Therefore, the area of the given honeycomb is approximately 10.4 millimeters square.