Question

Please help and show workings!

Answer 1

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 :)

Answer 2

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