The common length of the sides equals the radius of the circumscribed circle or circumcircle, which equals 2 3.

It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). Transfer the line segment AB four times on the circumscribed circle and connect the corner points.Ī regular hexagon is defined as a hexagon that is both equilateral and equiangular.

You can divide to get the simplified ratio (divide both sides by 8 or divide both sides by 6.92820320275509 - I divided by both, and my best 4 decimal round was the latter as we get a nice 1.When the side length AB is given, drawing a circular arc from point A and point B gives the intersection M, the center of the circumscribed circle. Technically the hexagon was 8 wide, so the one section of perfect tri has a height of 3.4641, but we would have to double that to get the height of the HEX this is NOT the correct ratio to 8, because this is not for the Hexagon. This works because a perfect HEX is a group of 6 perfect TRIs and a perfect TRI also has 3 equal sides, when cut in half to get a right triangle the measurement can be obtained as a ratio of a^2+b^2=c^2Ĭut right triangle has a base of 2 and a hypotenuse of 4 So if your hexagon is 7 Inches tall, multiply 7*1.154701 to get the perfect height of 8.082907 To create a perfect hexagon the ratio of Width and Height must be 1.154701:1 Move from point to point, it will never actually rotate to exactly 60 There is a problem with the 60 degree ration solution, as because it have to Resize object again, turn lock aspect ratio on. resize hexagon, turn off lock aspect ratio, set width (or longestīounding box edge) to 10cm and height (or shortest bounding box edge) toģ. Solution (Please test this on your machines and see if is solves theĢ. Powerpoint draws in 'points' and I suspect a rounding issue is (ie a hexagon with the long side of 10cm will equal 8.65cm, not 8.66cm as it PowerPoint however draws a hexagons at a ratio of 1:0.865

The ratio of a hexagon is 1:0.866 (and Yes a circle should touch every A true hexagon (equal sides and ofcourse angles) never has equal Height and

Perfect hexagon measurements