Answer :

Answer:

[tex]A=37.29[/tex]

Step-by-step explanation:

Since this is a regular polygon, it is composed of equally sized right triangles with vertices at: the center of the triangle, one of the polygon's vertices, and the middle of the side adjacent that vertex. Therefore, we can add the areas of the right triangles to get the total area of the polygon.

We can see that this pentagon (5-sided polygon) is composed of 10 right triangles with dimensions:

  • [tex]b=2.26[/tex]
  • [tex]h=3.3[/tex]

Therefore, its area is:

[tex]A_\triangle =\dfrac{1}{2}bh[/tex]

[tex]A_\triangle=\dfrac{1}{2}(2.26)(3.3)[/tex]

[tex]A_\triangle= 3.729[/tex]

So, the area of the regular polygon is:

[tex]A = 10\cdot A_\triangle[/tex]

[tex]A = 10\cdot 3.729[/tex]

[tex]\boxed{A=37.29}[/tex]

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