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Maslowich
2 years ago
9

Find the area of the regular polygon​

Mathematics
1 answer:
Y_Kistochka [10]2 years ago
8 0

Answer:

A = 374.123 ft^2

Step-by-step explanation:

First, lets calculate the perimeter:

Perimeter (p) = side length (s) * number of sides (n)

p = s * n

p = 12 * 6

p = 72

Next, lets find the apothem, which is the shortest length from any side to the middle. It's like the radius in a circle, but more complicated.

Apothem (a) = side length (s) / ( 2 * tan(180/number of sides (n)) )

a = \frac{s}{2 * tan (\frac{180}{n} )}

a = \frac{12}{2 * tan (\frac{180}{6} )}

a = \frac{12}{2 * \frac{\sqrt{3} }{3}}

a = \frac{12}{\frac{2\sqrt{3} }{3}}

a = \frac{12*3}{2\sqrt{3}}

a = \frac{6*3}{\sqrt{3}}

a = \frac{18}{\sqrt{3}}

Now, finally, to find the area of a regular polygon, we use the following equation:

Area (A) = ( apothem (a) * perimeter (p) ) / 2

A = \frac{a * p}{2}

A = \frac{\frac{18}{\sqrt{3} }  * 72}{2}

A = \frac{18}{\sqrt{3}}  * 36

A = \frac{640}{\sqrt{3}}

Turning into a decimal:

A = 374.123 ft ^2

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