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

1 Answer

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Answer:

192.6 square yards

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.

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Additional comment

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

  • determine an appropriate area formula for the given information
  • evaluate the formula for the given dimensions

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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