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Q: What is the ratio of the distance across corners to the distance across flats of a regular hexagon?

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In a regular hexagon, all sides are parallel to the one across from it. In other hexagons, this need not be the case.

___________ /\ \ / \ \ / \ \ / \\ / \ / \ : : : : : : \ / \ / \ / \____________/ ___________ /\ \ / \ \ / \ \ / \\ / \ / \ : : : : : : \ / \ / \ / \____________/

3/2*(shortest distance across the flats, passing through the center)*(length of one flat)

if it's a regular room with square walls run two pieces of string. one from opposing corners top to bottom across the room. and the other the same in different corners. where they cross is the centre.

2*((flat dist/2)/0.866) Or in words: Take half the flat distance, divide that by 0.866, multiply the result by 2. You can derive this yourself by drawing a hexagon and drawing in the lines you want through the exact center of the hexagon. You will discover this makes two right triangles, the hypotenuses of which are the "across corners", and the "long sides" of which are the "across flats". By inspection, there are 12 of these triangles, meaning the small angle of each is 30 degrees. The cosine of 30 degrees is 0.866, which is the ratio of each triangle's "long side" to their hypotenuse. Do the math and you will come up with the formula above. Cheers!

The longest distance across a circle is its diameter

Each side of a hexagon must be 12.5 inches in order for the widest part to be 25 inches across.

45.6 across

The distance half way across a circle is the circle's radius.radias

the distance across the middle is the radius and whole distance across it is the diameter

The distance half way across a circle is the circle's radius.radias

The distance across the diamond is 114.6 feet.

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