This result is because the volume of a sphere is the largest of any other object for a given surface area. When you create a bubble using water, soap, and some of your own breath, it always has a spherical shape. On top of that, the regular 6-sided shape has the smallest perimeter for the biggest area among these surface-filling polygons, which makes it very efficient.Ī fascinating example in this video is that of the soap bubbles. Another important property of regular hexagons is that they can fill a surface with no gaps between them (along with regular triangles and squares). This is a significant advantage that hexagons have. The way that 120º angles distribute forces (and, in turn, stress) amongst 2 of the hexagon sides makes it a very stable and mechanically efficient geometry. For a full description of the importance and advantages of regular hexagons, we recommend watching this video. The 120º angle is the most mechanically stable of all, and coincidentally it is also the angle at which the sides meet at the vertices when we line up hexagons side by side. And there is a reason for that: the hexagon angles. Try to use only right triangles or maybe even special right triangles to calculate the area of a hexagon! Diagonals of a hexagonįrom bee 'hives' to rock cracks through organic chemistry (even in the build blocks of life: proteins), regular hexagons are the most common polygonal shape that exists in nature. You can even decompose the hexagon in one big rectangle (using the short diagonals) and 2 isosceles triangles!įeel free to play around with different shapes and calculators to see what other tricks you can come up with. You could also combine two adjacent triangles to construct a total of 3 different rhombuses and calculate the area of each separately. In that case, you get two trapezoids, and you can calculate the area of the hexagon as the sum of them. For example, suppose you divide the hexagon in half (from vertex to vertex). If you want to get exotic, you can play around with other different shapes. We hope you can see how we arrive at the same hexagon area formula we mentioned before. After multiplying this area by six (because we have 6 triangles), we get the hexagon area formula: Where A₀ means the area of each of the equilateral triangles in which we have divided the hexagon. And the height of a triangle will be h = √3/2 × a, which is the exact value of the apothem in this case. This fact makes it much easier to calculate their area than if they were isosceles triangles or even 45 45 90 triangles as in the case of a square.įor the regular triangle, all sides are of the same length, which is the length of the side of the hexagon they form.

For the regular hexagon, these triangles are equilateral triangles. If you don't remember the formula, you can always think about the 6-sided polygon as a collection of 6 triangles. Alternatively, one can also think about the apothem as the distance between the center, and any side of the hexagon since the Euclidean distance is defined using a perpendicular line. You can view it as the height of the equilateral triangle formed by taking one side and two radii of the hexagon (each of the colored areas in the image above). Just as a reminder, the apothem is the distance between the midpoint of any side and the center. The formula for the area of a polygon is always the same no matter how many sides it has as long as it is a regular polygon: For those who want to know how to do this by hand, we will explain how to find the area of a regular hexagon with and without the hexagon area formula. The easiest way is to use our hexagon calculator, which includes a built-in area conversion tool. Each office space, showcasing diverse atmospheres as the changing scenery outside the windows, offers Genesis employees using autonomous seating a daily routine filled with excitement.We will now take a look at how to find the area of a hexagon using different tricks. During dusky evenings, the warm light from pendant lights reflects off wooden panels and iron structures, filling the office space with comfort and warmth. The sunlight penetrating deeply during the daytime interacts with wooden furniture and glass shelves, creating varied shadows that bring dynamism to the space. Living spaces where employees dwell and interact exude a contrasting atmosphere with the vertical-horizontal iron structure ceiling, featuring exposed wooden furniture and small rooms surrounded by wooden panels, crafting a warm and cozy ambiance. Warm Atmosphere Created by Light Reflecting on Wooden Furniture - Upon entering the office, one is greeted by a 5-meter high ceiling and 400 silver pendants adorning the expansive ceiling, creating an overwhelming first impression.

Radial corner wall shelf