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Pythagorean theorem in 3D

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Each vertical cross-section of the triangular prism shown below is an isosceles triangle.
A triangular prism with a vertical height of h units, a base of six units, and a slant height of three square root two units.
What is the vertical height, h, of the triangular prism?
Round your answer to the nearest tenth.
The height is
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0.75
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4