2026 DSS P1 Q6

2026 DSS P1 Q6

Secondary 4
7 marks

A right pyramid has a square base with diagonal \(2+\sqrt8\) cm.

The volume of the pyramid is \(10+6\sqrt2\) cm\(^3\).

Without using a calculator,

  1. show that the area, in cm\(^2\), of the square base is \(6+4\sqrt2\),[3]
  2. find the height, in cm, of the pyramid in the form \(c+d\sqrt2\), where \(c\) and \(d\) are integers.[4]

Solution:

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Answer:(a) \(6+4\sqrt2\) cm\(^2\). (b) \(9-3\sqrt2\) cm; \(c=9,d=-3\).

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