2025 SST PRELIMS P1 Q13

2025 SST PRELIMS P1 Q13

Secondary 4
4 marks

A star is made from regular hexagon \(ABCDEF\), centre \(X\), surrounded by equilateral triangles. \(\overrightarrow{OA}=2\mathbf a\) and \(\overrightarrow{OB}=2\mathbf b\).

  1. Express in terms of (mathbf a) and/or (mathbf b), in simplest form:
    1. \(\overrightarrow{OR}\).[1]
    2. \(\overrightarrow{FC}\).[1]
  2. When \(|\mathbf a|=6\) units, find the perimeter of the star \(OATFSERDQCPBO\).[2]

Solution:

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Answer:(a)(i) \(4\mathbf a+4\mathbf b\) (ii) \(4\mathbf b-4\mathbf a\) (b) \(144\) units

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