Multiple choice

The area of a square inscribed a circle with radius 14 cm is............ ${ Cm }^{ 2 }$

  1. 392

  2. 784

  3. 196

  4. 98
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A Correct answer
Explanation

A square inscribed in a circle has a diagonal equal to the diameter of the circle. Diameter = 2 * 14 = 28 cm. Area of square = (diagonal^2) / 2 = (28 * 28) / 2 = 784 / 2 = 392.

AI explanation

When a square is inscribed in a circle, the diagonal of the square equals the diameter of the circle. The diameter is 2 * 14 = 28 cm. Using the relation between side and diagonal, d = a * sqrt(2), we get a = 28 / sqrt(2) = 14 * sqrt(2) cm. The area of the square is a^2, which is (14 * sqrt(2))^2 = 196 * 2 = 392 sq cm.

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