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The diagonal of a square is 10 cm. What is the area of the square?
- a)50 cm²
- b)100 cm²
- c)200 cm²
- d)25 cm²
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The diagonal of a square is 10 cm. What is the area of the square?a)50...
Understanding the Square's Diagonal
The diagonal of a square is a line segment that connects two opposite corners. In this case, the diagonal measures 10 cm.
Relationship Between Diagonal and Side Length
To find the area of the square, we first need to determine the length of one side (s) using the relationship between the diagonal (d) and the side length:
- The formula for the diagonal of a square is given by:
- d = s√2
- Rearranging this formula to find the side length:
- s = d / √2
Calculating the Side Length
Given that the diagonal is 10 cm, we can substitute this value into the formula:
- s = 10 / √2
- s = 10 / 1.414 (approximately)
- s ≈ 7.07 cm
Finding the Area of the Square
Now that we have the side length, we can calculate the area (A) of the square using the formula:
- A = s²
Substituting the side length we calculated:
- A ≈ (7.07)²
- A ≈ 50 cm²
Conclusion
Therefore, the area of the square is approximately 50 cm², which corresponds to option 'A'.
The diagonal of a square is a line segment that connects two opposite corners. In this case, the diagonal measures 10 cm.
Relationship Between Diagonal and Side Length
To find the area of the square, we first need to determine the length of one side (s) using the relationship between the diagonal (d) and the side length:
- The formula for the diagonal of a square is given by:
- d = s√2
- Rearranging this formula to find the side length:
- s = d / √2
Calculating the Side Length
Given that the diagonal is 10 cm, we can substitute this value into the formula:
- s = 10 / √2
- s = 10 / 1.414 (approximately)
- s ≈ 7.07 cm
Finding the Area of the Square
Now that we have the side length, we can calculate the area (A) of the square using the formula:
- A = s²
Substituting the side length we calculated:
- A ≈ (7.07)²
- A ≈ 50 cm²
Conclusion
Therefore, the area of the square is approximately 50 cm², which corresponds to option 'A'.
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Community Answer
The diagonal of a square is 10 cm. What is the area of the square?a)50...
Let the side be s and diagonal d = 10 cm.
For a square, d = s√2, so s = d/√2 = 10/√2 = 5√2 cm.
Area = s2 = (5√2)2 = 25×2 = 50 cm².
Therefore, the area is 50 cm².
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The diagonal of a square is 10 cm. What is the area of the square?a)50 cm²b)100 cm²c)200 cm²d)25 cm²Correct answer is option 'A'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The diagonal of a square is 10 cm. What is the area of the square?a)50 cm²b)100 cm²c)200 cm²d)25 cm²Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diagonal of a square is 10 cm. What is the area of the square?a)50 cm²b)100 cm²c)200 cm²d)25 cm²Correct answer is option 'A'. Can you explain this answer?.
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