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erastova [34]
3 years ago
12

Please help and show workings!

Mathematics
2 answers:
Tomtit [17]3 years ago
7 0

Answer:

162\sqrt{3}

Step-by-step explanation:

The equation for finding the area of a hexagon with a side length is

(s^23\sqrt{3} )/2

insert 6\sqrt{3}

and you are left with 162\sqrt{3}

Hope that helps :)

White raven [17]3 years ago
7 0

Answer:

\displaystyle E)\: 162 \sqrt{3}

Step-by-step explanation:

we are given a side a polygon

and said to figure out the area

recall the formula of regular polygon

\displaystyle \:  \frac{ {na}^{2} }{4}  \cot \left( \frac{ {180}^{ \circ} }{n}  \right)

where a represents the length of a side

and n represents the number of sides

the given shape has 6 sides

and has a length of \displaystyle 6\sqrt{3}

so our n is 6 and a is 6√3

substitute the value of n and a:

\displaystyle \:  \frac{ {6 \cdot \:( 6 \sqrt{3} })^{2} }{4}  \cot \left( \frac{ {180}^{ \circ} }{6}  \right)

reduce fraction:

\displaystyle \:  \frac{ {6 \cdot \:( 6 \sqrt{3} })^{2} }{4}  \cot \left( \frac{ { \cancel{180}^{ \circ}} ^{ {30}^{ \circ} }  }{ \cancel{6 \: }  } \right)

\displaystyle \:  \frac{6 \cdot \: (6 \sqrt{ {3} } {)}^{2}  }{4}  \cot( {30}^{ \circ} )

simplify square:

\displaystyle \:  \frac{6 \cdot \: 36 \cdot \: 3  }{4}  \cot( {30}^{ \circ} )

reduce fraction:

\displaystyle \:  \frac{6 \cdot \:  \cancel{36} \:  ^{9}  \cdot \: 3  }{ \cancel{ 4 \: }  } \cot( {30}^{ \circ} )

\displaystyle \: 6 \cdot \: 9 \cdot \: 3 \cot( {30}^{ \circ} )

simplify multiplication:

\displaystyle \: 162\cot( {30}^{ \circ} )

recall unit circle:

\displaystyle \: 162 \sqrt{3}

hence, our answer is E

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