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Calculation of the diagonals in
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A square with the side length of a = 5 cm is given as an example.
A of
The length of the side of
è
d = 2 ·
Translated, this means: We know the area (A) of the big
square (a ∙ a). In this example, 5 ∙ 5 = A = 25. In other words, the length
of the side is the root of 25. The Diagonal divides the square in two
equally sized triangles. This means, that the area of the red triangle 25:2
is therefore 12,5. If this triangle is divided once again into two equally
sized parts, it can be made a square, in this case, the green square.
Consequently, the green square has the same area as the red triangle and as
a consequence, half of the big square also (a2). The area of the
green triangle is 12,5. To get the length of the side, the root of 12,5 is
needed. The diagonal is twice as long as the side of the green square. So
the diagonal is 2 ∙
Another easier way A square with the side length a is given.
d² = a² · 2
The length of the side of a² =
Surface of d² = a² · 2
The length of side d² =
= a ·
Formula:
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=
=
12,5
