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A square , whose side is 4 meters has its corner cut away so as to form an octagon with all sides equal . Find the length of each side of the octagon (in meters)?
Most Upvoted Answer
A square , whose side is 4 meters has its corner cut away so as to for...
Solution:
Given:
Side length of the square = 4 meters
To find:
Length of each side of the octagon
Explanation:
Step 1: Calculate the length of the diagonal of the square
The diagonal of a square can be calculated using the Pythagorean theorem. Since the square has equal sides, we can use the formula:
Diagonal = side × √2
Substituting the given value:
Diagonal = 4 × √2
Step 2: Calculate the length of the octagon side
To find the length of each side of the octagon, we need to consider that the octagon is formed by cutting off the corners of the square. Since the octagon has equal sides, we can divide the square into 8 congruent isosceles triangles.
Step 3: Calculate the length of the triangle sides
In each isosceles triangle, the equal sides are the side of the square and the side of the octagon. Let's consider one of these triangles:
Step 4: Calculate the length of the octagon side
We can use the Pythagorean theorem to find the length of the octagon side. Let's denote the length of the octagon side as x. Using the triangle formed in Step 3, we have:
(side of square)^2 = (side of octagon)^2 + (side of triangle)^2
Substituting the values:
4^2 = x^2 + (2x)^2
16 = x^2 + 4x^2
16 = 5x^2
x^2 = 16/5
x = √(16/5)
Therefore, the length of each side of the octagon is approximately 2.52 meters.
Given:
Side length of the square = 4 meters
To find:
Length of each side of the octagon
Explanation:
Step 1: Calculate the length of the diagonal of the square
The diagonal of a square can be calculated using the Pythagorean theorem. Since the square has equal sides, we can use the formula:
Diagonal = side × √2
Substituting the given value:
Diagonal = 4 × √2
Step 2: Calculate the length of the octagon side
To find the length of each side of the octagon, we need to consider that the octagon is formed by cutting off the corners of the square. Since the octagon has equal sides, we can divide the square into 8 congruent isosceles triangles.
Step 3: Calculate the length of the triangle sides
In each isosceles triangle, the equal sides are the side of the square and the side of the octagon. Let's consider one of these triangles:
Step 4: Calculate the length of the octagon side
We can use the Pythagorean theorem to find the length of the octagon side. Let's denote the length of the octagon side as x. Using the triangle formed in Step 3, we have:
(side of square)^2 = (side of octagon)^2 + (side of triangle)^2
Substituting the values:
4^2 = x^2 + (2x)^2
16 = x^2 + 4x^2
16 = 5x^2
x^2 = 16/5
x = √(16/5)
Therefore, the length of each side of the octagon is approximately 2.52 meters.
Community Answer
A square , whose side is 4 meters has its corner cut away so as to for...
2 m
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A square , whose side is 4 meters has its corner cut away so as to form an octagon with all sides equal . Find the length of each side of the octagon (in meters)?
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A square , whose side is 4 meters has its corner cut away so as to form an octagon with all sides equal . Find the length of each side of the octagon (in meters)? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about A square , whose side is 4 meters has its corner cut away so as to form an octagon with all sides equal . Find the length of each side of the octagon (in meters)? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square , whose side is 4 meters has its corner cut away so as to form an octagon with all sides equal . Find the length of each side of the octagon (in meters)?.
A square , whose side is 4 meters has its corner cut away so as to form an octagon with all sides equal . Find the length of each side of the octagon (in meters)? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about A square , whose side is 4 meters has its corner cut away so as to form an octagon with all sides equal . Find the length of each side of the octagon (in meters)? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square , whose side is 4 meters has its corner cut away so as to form an octagon with all sides equal . Find the length of each side of the octagon (in meters)?.
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