thought this would be an appropriate place to share some of what i thought was interesting information to do with the area of a triangle and how numbers co-relate.

To round off a square to 100cm square, one quarter of that area is 25cm square, (10cmx10cm =100/(div)25%=25cm), the area of a  right angle triangle with sides measuring ~7.0710cm,  equals ~25% of 100cm square,  25cm square of area,  (7.0710/2=3.5355 x7.0710=24.9995205).

7.5937 if it is an equilateral triangle.

it is a standard size i use,  a handy measurement if you use templates for construction because it in  some way represents a metric increment,

thanks,

Kim

(the formula i used is half the base times the height,  unless im mistaken i recall that is the correct formula?  though i am not a full time mathamatician.  for the equalateral triangle i used a web based polygon area calculator.)

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## Discussions

i saw a doco on egyptian building they showed a variation of a water level,
The device is calibrated by the base point(s) located on the surface of water and the position of the string is marked, (probably with a scribe back in the day). perhaps a stonemasons level.

All you've done is to cut your square along the diagonals. Each of the resulting quarters is obviously a right triangle, with hypotenuse equal to the side of the square, and sides both equal to 1/sqrt(2) times the hypotenuse.

It's a pity you just copied the output of some Web-based calculator, rather than learning the underlying geometrical relationships involved.