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Area, SM-Bank 040

Cabins are being built at a camp site.

The dimensions of the front of each cabin are shown in the diagram below.
 

The walls of each cabin are 2.4 m high.

The sloping edges of the roof of each cabin are 2.4 m long.

The front of each cabin is 4 m wide.

The pependicular height the triangular shaped roof is `h` metres.

  1. Use Pythagoras to show that the value of \(h\) is 1.33 m, correct to two decimal places.  (2 marks)

  2. Calculate the total area of the front of the cabin.  (2 marks)

Show Answers Only

a.    \(1.33\ \text{m}\)

b.    \(12.26\ \text{m}^2\)

Show Worked Solution

a.    \(\text{Using Pythagoras:  }a^2+b^2=c^2\)

\(h^2+2^2\) \(=2.4^2\)
\(h^2\) \(=2.4^2-2^2\)
\(h^2\) \(=1.76\)
\(h\) \(=\sqrt{1.76}\)
  \(=1.326\dots\)
  \(\approx 1.33\ \text{m}\ (2\ \text{d.p.}\)

 

b.   \(\text{Area of walls and roof}\)

\(=\text{Area of Rectangle}+\text{Area of Triangle}\)

\(=4\times 2.4+\dfrac{1}{2}\times 4\times 1.33\)

\(=12.26\ \text{m}^2\)