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The area of a square inscribed in a circle, whose diagonal is 16 cm, is:
  • a)
    256 cm2
  • b)
    64 × √2 cm2
  • c)
    64 cm2
  • d)
    128 cm2
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The area of a square inscribed in a circle, whose diagonal is 16 cm, i...
Given:
Diagonal of the square = 16 cm

Concept used:
Diagonal of a square = a√2
Area of a square = a2
where a is the length of its side.
Calculation:
Side of the square = 16 ÷ √2 = 8√2
Area of the square = (8√2)2 = 128 cm2
∴ The area of a square inscribed in a circle, whose diagonal is 16 cm, is 128 cm2.
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Community Answer
The area of a square inscribed in a circle, whose diagonal is 16 cm, i...
The diagonal of the square is equal to the diameter of the circle.

Let's find the side length of the square first.
The diagonal of the square forms a right triangle with two sides equal to the side length of the square.
Using the Pythagorean theorem, we have:
(diagonal)^2 = (side length)^2 + (side length)^2
16^2 = 2(side length)^2
256 = 2(side length)^2
(side length)^2 = 256/2
(side length)^2 = 128
side length = √128 = 8√2

Now, let's find the area of the square.
Area of a square = (side length)^2
Area of the square = (8√2)^2
Area of the square = 64*2
Area of the square = 128 cm^2

So, the area of the square inscribed in the circle is 128 cm^2.
The correct answer is b) 128 cm^2.
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The area of a square inscribed in a circle, whose diagonal is 16 cm, is:a)256 cm2b)64 × √2cm2c)64 cm2d)128 cm2Correct answer is option 'D'. Can you explain this answer?
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