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A square can be inscribed in a circle of radius 'r' centimetre find the area of square?
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A square can be inscribed in a circle of radius 'r' centimetre find th...
Understanding the Relationship Between a Square and a Circle
When a square is inscribed in a circle, the vertices of the square touch the circle. The circle's radius is the distance from the center of the circle to any point on the circle, which is also the distance from the center to any vertex of the square.
Finding the Side Length of the Square
1. Diagonal of the Square:
The diagonal of the square can be calculated using the relationship between the radius and the diagonal:
- Diagonal = 2 * radius (r)
2. Using the Diagonal to Find the Side Length:
The diagonal (d) of the square can also be related to its side length (s) using the formula:
- d = s * √2
Therefore, we can solve for the side length:
- s = d / √2 = (2 * r) / √2 = r * √2
Calculating the Area of the Square
1. Area Formula:
The area (A) of a square is given by:
- A = s²
2. Substituting the Side Length:
Using the side length we found:
- A = (r * √2)² = r² * 2
Final Area of the Square
Thus, the area of the square inscribed in a circle of radius 'r' is:
- Area = 2 * r² square centimeters
This formula allows you to determine the area of the square based on the circle's radius efficiently!
When a square is inscribed in a circle, the vertices of the square touch the circle. The circle's radius is the distance from the center of the circle to any point on the circle, which is also the distance from the center to any vertex of the square.
Finding the Side Length of the Square
1. Diagonal of the Square:
The diagonal of the square can be calculated using the relationship between the radius and the diagonal:
- Diagonal = 2 * radius (r)
2. Using the Diagonal to Find the Side Length:
The diagonal (d) of the square can also be related to its side length (s) using the formula:
- d = s * √2
Therefore, we can solve for the side length:
- s = d / √2 = (2 * r) / √2 = r * √2
Calculating the Area of the Square
1. Area Formula:
The area (A) of a square is given by:
- A = s²
2. Substituting the Side Length:
Using the side length we found:
- A = (r * √2)² = r² * 2
Final Area of the Square
Thus, the area of the square inscribed in a circle of radius 'r' is:
- Area = 2 * r² square centimeters
This formula allows you to determine the area of the square based on the circle's radius efficiently!
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A square can be inscribed in a circle of radius 'r' centimetre find the area of square?
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A square can be inscribed in a circle of radius 'r' centimetre find the area of square? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A square can be inscribed in a circle of radius 'r' centimetre find the area of square? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square can be inscribed in a circle of radius 'r' centimetre find the area of square?.
A square can be inscribed in a circle of radius 'r' centimetre find the area of square? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A square can be inscribed in a circle of radius 'r' centimetre find the area of square? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square can be inscribed in a circle of radius 'r' centimetre find the area of square?.
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