A = (5\sqrt{2})^2 = 25 \times 2 = 50 \text{ square cm}

February 22, 2026

$A = (5\sqrt{2})^2 = 25 \times 2 = 50 \text{ square cm}$

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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:
Thus, the area of the larger square is \(\boxed{50}\) square cm.
An equilateral triangle has a perimeter of 18 cm. If each side is increased by 2 cm, by how many square centimeters does the area increase?
The side length \(s\) of the original equilateral triangle is:

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