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Vaselesa [24]
3 years ago
6

The regular hexagon has a radius of 4 in.

Mathematics
2 answers:
AleksAgata [21]3 years ago
6 0
\bf \textit{area of a regular polygon}=\cfrac{1}{2}nR^2\cdot  sin\left(\frac{360}{n}  \right)
\\ \quad \\ \quad \\
\begin{cases}
n=\textit{number of sides in the polygon}\\
R=\textit{radius of the polygon}
\end{cases}

so, sides= n= 6
radius = R = 4
\bf \textit{area of a regular polygon}=\cfrac{1}{2}nR^2\cdot  sin\left(\frac{360}{n}  \right)
\\ \quad \\ \quad \\
\begin{cases}
n=\textit{number of sides in the polygon}\\
R=\textit{radius of the polygon}
\end{cases}
\\ \quad \\ \quad \\
\cfrac{1}{2}6\cdot 4^2\cdot  sin\left(\frac{360}{6}  \right)\implies 
\cfrac{1}{2}\cdot 96\cdot  sin\left(60^o  \right)
\\ \quad \\
48\cdot  sin\left(60^o  \right)
cestrela7 [59]3 years ago
3 0

we know that

The Area of a Regular Polygon is equal to the formula

A=\cfrac{1}{2}nr^2\cdot sin\left(\frac{360}{n} \right)

where

n is number of sides in the polygon

r is the radius of the polygon

In this problem

the regular polygon is a hexagon with radius of 4 in

So

n=6\\ r=4 in

Substitute the value of n and r in the formula above

A=\cfrac{1}{2}*6*4^2\cdot sin\left(\frac{360}{6} \right)\\ \\A=\cfrac{96}{2}* sin(60) \\ \\ A=\frac{96}{2} *\frac{\sqrt{3}}{2}  \\ \\ A=24\sqrt{3} \\ \\ A=41.57 in^{2}

therefore

the answer is the option

42 in.2

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