Peter has built a gazebo, whose shape is a regular heptagon, with a side length of $1$ unit. He has also built a pathway around the gazebo, of constant width $1$ unit, as shown below. (Every point on the ground that is within $1$ unit of the gazebo and outside the gazebo is covered by the pathway.) Find the area of the pathway.

Area of pathway = 10.375 unit²

Step-by-step explanation:

Given - Peter has built a gazebo, whose shape is a regular heptagon, with

             a side length of 1 unit. He has also built a pathway around the

             gazebo, of constant width 1 unit, as shown below.

To find -  Find the area of the pathway.

Proof -

Central angle = = 51.43°

Now,

Central angle / 2 = = 25.71°

And

height = = 1.038

Now,

Inner area of gazebo = 7··1·(1.038) = 3.634 unit²

Outer area of gazebo = ()²·(3.364) = 14.009 unit²

∴ we get

Area of pathway = Outer area - Inner area

                            = 14.009 - 3.634

                            = 10.375 unit²

⇒Area of pathway = 10.375 unit²

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step-by-step explanation:

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