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Question Number 66852 by John Kaloki Musau last updated on 20/Aug/19

Commented by John Kaloki Musau last updated on 20/Aug/19

The cross-section of a head of a bolt is the form of a regular hexagon as shown in the figure below. Determine the area of the cross-section.

Commented by John Kaloki Musau last updated on 20/Aug/19

$$Theansweris86.62{cm}^2$$$$\mathit{p}\mathit{l}\mathit{e}\mathit{a}\mathit{s}\mathit{e}\mathrm{show}\mathrm{me}\mathrm{how}\mathrm{to}\mathbf{do}\mathbf{it}$$

Commented by Prithwish sen last updated on 20/Aug/19

$$\mathrm{In}\mathrm{a}\mathrm{regular}\mathrm{hexagon}\mathrm{there}\mathrm{are}6\mathrm{equilateral}$$$$\mathrm{triangles}\mathrm{of}\mathrm{height}5\mathrm{cm}$$$$\therefore \mathrm{each}\mathrm{side}=5\times \frac{2}{\sqrt{3}}\mathrm{cm}$$$$\therefore \mathrm{the}\mathrm{total}\mathrm{area}=6\times \frac{\sqrt{3}}{4}\times {\left(\frac{10}{\sqrt{3}}\right)}^2\mathrm{sq}.\mathrm{cm}$$$$=50\sqrt{3}\mathrm{sq}.\mathrm{cm}.=86.6\mathrm{sq}.\mathrm{cm}$$

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