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Volume, SM-Bank 064

  1. For the triangular prism above, use Pythagoras' Theorem to calculate the perpendicular height, \(x\), of the triangular face.  (2 marks)
  2. Using your answer from (a), calculate the volume of the prism in cubic millimetres.  (2 marks)
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a.    \(5\ \text{mm}\)

b.    \(480\ \text{mm}^3\)

Show Worked Solution
a.    \(a^2+b^2\) \(=c^2\)
  \(x^2+12^2\) \(=13^2\)
  \(x^2\) \(=13^2-12^2\)
  \(x^2\) \(=25\)
  \(x\) \(=\sqrt{25}=5\)

 
\(\therefore\ \text{The perpendicular height of the triangle is }5\ \text{mm}\)
 

b.    \(V\) \(=Ah\)
    \(=\Big(\dfrac{1}{2}\times 12\times 5\Big)\times 16\)
    \(=30\times 16\)
    \(=480\ \text{mm}^3\)