Class 7 Exam > Class 7 Questions > A square , whose side is 4 meters has its cor...
Start Learning for Free
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
Attention Class 7 Students!
To make sure you are not studying endlessly, EduRev has designed Class 7 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 7.
|
Explore Courses for Class 7 exam
|
|
Similar Class 7 Doubts
Top Courses for Class 7View all
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)?
Question Description
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)?.
Solutions 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)? in English & in Hindi are available as part of our courses for Class 7.
Download more important topics, notes, lectures and mock test series for Class 7 Exam by signing up for free.
Here you can find the meaning of 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)? defined & explained in the simplest way possible. Besides giving the explanation of
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 detailed solution 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)? has been provided alongside types of 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)? theory, EduRev gives you an
ample number of questions to practice 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)? tests, examples and also practice Class 7 tests.
|
|
Explore Courses for Class 7 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup