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If the diagonal of a square is doubled. How does the area of the square change?

Correct answer: A. Becomes fourfold

  • A. Becomes fourfold
  • B. Becomes threefold
  • C. Becomes twofold
  • D. none of the above

Explanation

For a square, diagonal d = side × √2, so doubling the diagonal also doubles the side. Since area is proportional to the square of the side, the area changes by 2² = 4 and becomes fourfold; option c, twofold, treats area as proportional to side length rather than its square.

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Area measures the surface enclosed by two-dimensional figures, while volume measures the space occupied by three-dimensional solids. Problems use formulas for rectangles, triangles, circles, prisms, cylinders, cones, spheres, and composite figures, including unit conversion and the distinction between surface area, lateral area, and volume.

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