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find the area of a pentagon with an apothem of 7 centimeters

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If the side length of the pentagon is 19.27 centimeters. Then the area of the pentagon will be 337.225 square cm.

What is a polygon?

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

The apothem of the pentagon is 7 cm.

Then the area of the pentagon will be

[tex]\rm Area = 5 \times \dfrac{1}{2} \times apothem \times side \ length[/tex]

The side length of the pentagon will be

[tex]\rm Side \ length = 2 \times 7 \tan 54^o \\\\Side \ length = 19.27\ cm[/tex]

Then the area will be

[tex]\rm Area = 5 \times \dfrac{1}{2} \times 7\times 19.27\\\\Area = 337.225[/tex]

More about the polygon link is given below.

https://brainly.com/question/17756657

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