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Area, SMB-016

A square pyramid with a perpendicular height of 8 metres is pictured below.
 

  1. Using Pythagoras, calculate the slant height of the pyramid.   (2 marks)
  1. Find the total surface area of the pyramid, including its base, to the nearest square metre.   (2 marks)
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i.    \(10\ \text{m} \)

ii.    \(384\ \text{m}^2 \)

Show Worked Solution

i.    \(\text{Let}\ \ s =\ \text{slant height}\)

\(s^2\) \(=6^2 + 8^2\)  
  \(=100\)  
\(s\) \(=10\ \text{m}\)  

 

ii.    \(\text{SA}\) \(= (12 \times 12) + 4 \times (\dfrac{1}{2} \times 12 \times 10)\)  
  \(=144 + 4(60) \)  
  \(=384\ \text{m}^2 \)