A regular hexagon has side length 3.0 cm and height 5.2 cm as shown in the diagram above.
Calculate the area of the hexagon, giving your answer correct to one decimal place. (3 marks)
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Show Worked Solution
| \(\text{Area of rectangle}\) | \(=3.0\times 5.2\) |
| \(= 15.6\ \text{cm}^2\) |
\(\text{Using Pythagoras to find}\ h:\)
| \(3.0^2\) | \(=2.6^2+h^2\) |
| \(h^2\) | \(=9-6.76\) |
| \(h^2\) | \(=2.24\) |
| \(h\) | \(=1.496\dots\) |
\(\text{Area of}\ \Delta ABC\)
\(=\dfrac{1}{2}\times bh\)
\(=\dfrac{1}{2}\times 5.2\times 1.496\dots\)
\(= 3.891\dots\ \text{cm}^2\)
\(\therefore\ \text{Area of hexagon}\)
\(=15.6+(2\times 3.891\dots)\)
\(=23.382\dots\approx 23.4\ \text{cm}^2\)