A shed has the shape of a prism. Its front face, \(AOBCD\), is shaded in the diagram below.
\(ABCD\) is a rectangle and \(M\) is the midpoint of \(AB\).
\(\Delta AMO\) is right angled and the length of \(AM\) is 3 metres.
- Using Pythagoras' Theorem find the length of \(OM\). (2 marks)
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- Calculate the area of the front face of the shed, \(AOBCD\), in square metres. (2 marks)
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- Find the volume of the shed in cubic metres. (1 mark)
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Show Worked Solution
| a. |  |
\(\text{In}\ \Delta AOM,\ \text{using Pythagoras:}\)
| \(OM^2+AM^2\) | \(=OA^2\) |
| \(OM^2+3^2\) | \(=3.4^2\) |
| \(OM^2\) | \(=3.4^2-3^2\) |
| \(OM\) | \(=\sqrt{3.4^2-3^2}\) |
| \(=\sqrt{2.56}\) | |
| \(=1.6\ \text{m}\) |
b. \(\text{Area of front face of shed}\)
\(=\text{Area}\ \Delta AOB+\text{Area}\ ABCD\)
\(=\dfrac{1}{2}\times 1.6\times 6+2.2\times 6\)
\(=18\ \text{m}^2\)
| c. | \(V\) | \(=Ah\) |
| \(=18\times 10\) | ||
| \(=180\ \text{m}^3\) |