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The diagonal of a square is 4√2cm. The diagonal is another square whose area is double that of the first square is__________?

Correct answer: A. 8cm

  • A. 8cm
  • B. 8√2cm
  • C. 16cm
  • D. 4√2cm

Explanation

For a square, diagonal² = 2 x area. The first diagonal is 4√2 cm, so its area is (4√2 cm)² ÷ 2 = 16 square centimetres. A square with double this area has area 32 square centimetres, so its diagonal is √(2 x 32 square centimetres) = 8 cm. The likely mistake is option b, which doubles the diagonal instead of recognising that area is proportional to diagonal².

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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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