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Area, SM-Bank 055

The square below has a diagonal of 12 metres.

  1. Use Pythagoras' Theorem to calculate the side length of the square. Give your answer in exact surd form.  (2 marks)


  2. Calculate the are of the square correct to one decimal place.  (2 marks)

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a.    \(\sqrt{72}\ \text{m}\)

b.    \(72\ \text{m}^2\)

Show Worked Solution

a.    \(\text{Using Pythagoras to find the side length of the square:}\)

\(a^2+b^2\) \(=c^2\)
\(a^2+a^2\) \(=12^2\)
 \(2a^2\) \(=144\)
\(a^2\) \(=\dfrac{144}{2}=72\)
 \(a\) \(=\sqrt{72}\ \text{m}\)

b.   

\(\text{Area}\) \(=s^2\)
  \(=(\sqrt{72})^2\)
  \(=72\ \text{m}^2\)