Find the area of a regular pentagon with a radius of 9 yds. show all six steps.

  192.6 square yards

Step-by-step explanation:

The area of a regular pentagon can be found using the formula for any regular polygon.

  A = (n/2)r²·sin(360°/n) . . . . radius r, n sides

For a pentagon, the number of sides is 5, so this becomes ...

  A = 2.5r²·sin(72°)

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Using the given value of radius, the area is ...

  A = 2.5(9 yd)²·sin(72°) = 2.5 · 81 · 0.951057 yd²

  A ≈ 202.5 · 0.951057 yd²

  A ≈ 192.589 yd²

The area of the pentagon is about 192.6 square yards.

Additional comment

We're not sure what "six steps" you're supposed to follow. The necessary steps appear to be ...

Here, the formula for a pentagon can be simplified somewhat by precomputing the value of 2.5×sin(72°) ≈ 2.37764129074. Then the formula for the area is ...

  A = 2.37764129074·r² . . . . . area of regular pentagon with radius r

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step-by-step explanation: