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What is the area of a square inscribed in a circle of radius 10 cm?

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Question: What is the area of a square inscribed in a circle of radius 10 cm?

Options:

  1. 100 cm²
  2. 200 cm²
  3. 150 cm²
  4. 50 cm²

Correct Answer: 200 cm²

Solution: 

The diagonal of the square is equal to the diameter of the circle, which is 20 cm. Side of the square = diagonal / √2 = 20 cm / √2 = 10√2 cm. Area = (10√2 cm)² = 200 cm².

What is the area of a square inscribed in a circle of radius 10 cm?

Practice Questions

Q1
What is the area of a square inscribed in a circle of radius 10 cm?
  1. 100 cm²
  2. 200 cm²
  3. 150 cm²
  4. 50 cm²

Questions & Step-by-Step Solutions

What is the area of a square inscribed in a circle of radius 10 cm?
  • Inscribed Shapes – Understanding the relationship between a square and a circle, specifically how the diagonal of the square relates to the diameter of the circle.
  • Pythagorean Theorem – Applying the theorem to find the side length of the square using the diagonal.
  • Area Calculation – Calculating the area of a square given its side length.
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