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?
Enough, already. You are being a pest with your multiple posts of the same question.
True. If I see 6-10 posts by the same person in a short time span, I figure that either it's a homework dump, or multiple posts of the same question. Either way, I'm starting to ignore the whole bunch.
Believe it or not, the volunteers who help with the questions also have a life. You could spend the interval working on it yourself, rather than reposting every five minutes.
To determine the length of the side of the resulting octagon, we can use the property that if a regular polygon is inscribed within a circle, the length of each side is equal to the radius of the circle.
Here's how to find the radius of the circle:
1. Start with the original square with side length 2m.
2. Draw the diagonal from one corner to the opposite corner of the square. This diagonal has a length of 2√2m (using the Pythagorean theorem).
3. The octagon is formed by cutting off the corners of the square, so the distance from the center of the square to each corner of the octagon is equal to the radius of the inscribed circle. This distance is equal to half the length of the diagonal, which is (√2)m.
4. Therefore, the length of each side of the resulting octagon is equal to the radius of the circle, which is (√2)m.
So, the length of the side of the resulting octagon is (√2)m.