The corners of the square, 2m. sides, are cut off to form a regular octagon. What is the length of the side of the resulting octagon?
To find the length of the side of the resulting octagon, we can proceed as follows:
1. Calculate the side length of the square:
Since the square has a side length of 2m, its perimeter is 4 * 2m = 8m.
2. Calculate the length of each cut-off corner of the square:
Since the corners are cut off to form an octagon, each cut-off corner will be an isosceles right triangle with legs of length equal to the side of the octagon.
Let's denote the side length of the octagon as 's'.
The hypotenuse of each cut-off corner triangle will be the side length of the square, which is 2m.
Using the Pythagorean theorem, we can find the length of each cut-off corner:
(s)^2 + (s)^2 = (2m)^2
2s^2 = 4m^2
s^2 = 4m^2 / 2
s^2 = 2m^2
s = sqrt(2m^2)
s = sqrt(2) * m
3. Calculate the side length of the resulting octagon:
Since an octagon has eight equal sides, the side length of the resulting octagon will be equal to the length of the cut-off corners of the square.
Therefore, the side length of the resulting octagon is sqrt(2) * m.
So, the length of the side of the resulting octagon is sqrt(2) multiplied by the side length of the original square.