The base of a regular pyramid is a hexagon. What is the area of the base of the pyramid? Express your answer in radical form.

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The base of a regular pyramid is a hexagon. What is the area of the base of the pyramid? Express your answer in radical form.

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Answer 1 · 2017-05-24T21:03:51

Area of hexagon is $216 \sqrt{3}$ $216sqrt(3)$ $c m^{2}$ $cm^2$

Explanation:

We know that the angle at $C$ $C$ is 30 degrees, so half of the base must be $\frac{12}{2}$ $12/2$ which is $6$ $6$ as $sin (\frac{π}{6}) = \frac{1}{2}$ $sin(pi/6)=1/2$ .
Finding $a$ $a$ is a matter of Pythagorean,

as such $a^{2} + 6^{2} = 12^{2}$ $a^2+6^2=12^2$

or $a^{2} = 144 - 36 = 108$ $a^2=144-36=108$ and

$a = \sqrt{108} = \sqrt{6 \times 6 \times 3} = 6 \sqrt{3}$ $a=sqrt108=sqrt(6xx6xx3)=6sqrt(3)$ .

Now, we have the height and half of the base, which means the area of $\frac{1}{6}$ $1/6$ th of the hexagon will be $\frac{1}{2} b h$ $1/2bh$ where $b = 12$ $b=12$ and $h = 6 \sqrt{3}$ $h=6sqrt3$ .

The area of the hexagon therefore will be $6 \times \frac{1}{2} b h$ $6xx1/2bh$ .

$= 6 \times \frac{1}{2} \times 12 \times 6 \sqrt{3} = 216 \sqrt{3}$ $=6xx1/2xx12xx6sqrt(3)=216sqrt(3)$ $c m^{2}$ $cm^2$

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The base of a regular pyramid is a hexagon. What is the area of the base of the pyramid? Express your answer in radical form.

1 Answer

Explanation:

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