First, calculate the diagonal of the square with side length 5 cm. Using the Pythagorean theorem, the diagonal \(d\) is given by:

February 22, 2026

$First, calculate the diagonal of the square with side length 5 cm. Using the Pythagorean theorem, the diagonal \(d\) is given by:$

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A circle with a diameter equal to the diagonal of a square with side length 5 cm is inscribed in a square. Find the area of the larger square.
d = \sqrt{5^2 + 5^2} = \sqrt{25 + 25} = \sqrt{50} = 5\sqrt{2} \text{ cm}
The diameter of the circle is equal to this diagonal, \(5\sqrt{2}\) cm. Since the circle is inscribed in a larger square, the side of the larger square is equal to the diameter of the circle. Thus, the side length of the larger square is \(5\sqrt{2}\) cm.
The area \(A\) of the larger square is:

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