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a regular heptagon has an apothem that is 3 inches in length. one of the sides has a length of 7 inches. what is the area of the heptagon?

Sagot :

The area of the Heptagon is 32.6

What is Heptagon?

A polygon having 7 sides and 7 angles are called a heptagon. The term "septagon" may also be used to refer to the heptagon. A heptagon is formed when all of its sides come together end to end. Therefore,

The heptagon's sides total seven.

What Is Meant by Apothem?

Apothem is a line traced from any polygon's center to one of its sides' midpoints.

The apothem formula, when the side length is given is:

[tex]a=\frac{S}{2 \tan \left(\frac{180}{n}\right)}[/tex]

Where,

a = apothem length

s = side length

n = number of sides of a polygon.

In the given question,

we have;

s = 7 inches;

a = 3 inches;

n = 7;

So,

The apothem, when the side length is given is:

[tex]a=\frac{S}{2 \tan \left(\frac{180}{n}\right)}[/tex]

[tex]a=\frac{3}{2 \tan \left(\frac{180}{7}\right)}[/tex]

so, The area of Heptagon is 7.[tex]\frac{3.7}{2}[/tex]

The area of the Heptagon is 32.6

To learn more about heptagon, visit:

https://brainly.com/question/5361966

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