Find the area of the regular 18-gon with a radius of 3 mm. Round to the nearest tenth.

Mathematics

1 answer:

marta [7]3 years ago

7 0

Answer:

this becomes 1/2 * 6 * tan(10) * 3 which results in the area of one of the isosceles triangles is equal to 1.586942826 square units. since there are 18 of these isosceles triangles in the polygon, then multiply this by 18 to get area of the polygon with 18 sides is equal to 28.56497087 square units.

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marshall27 [118]

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
&&(~ -2 &,& -2~) 
&&(~ 0 &,& 5~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-(-2)}{0-(-2)}\implies \cfrac{5+2}{0+2}\implies \cfrac{7}{2}
\\\\\\
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-2)=\cfrac{7}{2}[x-(-2)]
\\\\\\
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