Find the area of a regular nonagon (9-sided polygon) if the apothem is 4 cm long, and each side is14 cm.
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Answer:
[tex]252\text{ cm}^2[/tex]Explanation:
Here, we want to find the area of the polygon
Mathematically, we have that calculated as:
[tex]A\text{ = }\frac{n\times b\times a}{2}[/tex]where:
n is the number of sides of the polygon which is 9
b is the length of a side which is 14 cm
a is the length of the apothem which is 4 cm
Substituting the values, we have it that:
[tex]A\text{ = }\frac{9\times14\times4}{2}\text{ = 252 cm}^2[/tex]