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kvasek [131]
3 years ago
7

Find the area of a regular hexagon with the side length of 10 centimeters. Round to the nearest tenth

Mathematics
1 answer:
Romashka [77]3 years ago
8 0
Polygon area = n * side length^2 / 4 * tan(180/n)
where "n" = number of sides
hexagon area = 6 * 10^2 / 4 * tan(180/6)
hexagon area = 600 / 4 * tan(30)
hexagon  area = 600 / 4 * 0.57735
hexagon  area = <span> <span> <span> 259.8077422707 </span> </span> </span> square centimeters
hexagon  area = <span> 259.8 </span>square centimeters


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<em>Multiplying both sides by 16 we get:</em>

<em />256=3x^2<em />

<em>Dividing both sides by 3 we get:</em>

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Base=\frac{x}{2}\\\\Base=\frac{\frac{16}{\sqrt{3}}}{2} \\\\Base=\frac{8}{\sqrt{3}} \ m.

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<em>Thus, the height of triangle =  </em>\frac{12}{\sqrt{3}} \ m.<em />

Therefore, the base of triangle is  \frac{8}{\sqrt{3}} \ m and the height of triangle is  \frac{12}{\sqrt{3}} \ m.

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