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For that same pyramid, the area of the mid-height section compared with the base area is

  • A.one eighth
  • B.one quarter
  • C.one half
  • D.three quarters

Answer: B

Correct answer: one quarter

Areas scale as the square of the linear ratio, so a section at half the height has \[ \left(\tfrac{1}{2}\right)^2 = \tfrac{1}{4} \] of the base area. Halving the area would require a cut at \( 1/\sqrt{2} \) of the height from the apex, which is about 71 per cent of the way up rather than half.

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