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Simon has built a gazebo, whose shape is a regular heptagon, with a side length of 1 unit. He has also built a walkway 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 walkway.) Find the area of the walkway.

 May 27, 2020
 #1
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The area is 9.692.

 May 27, 2020
 #2
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The area of the walkway is   10.14159265 units squared.   smiley

 May 30, 2020
 #3
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The area of a square ABCE is 1 unit squared.

 

The area of the region CDE is 1/7 of the full circle with a radius of 1 unit.

 

The area of the walkway is  7 + pi = 10.14159265 u²   indecision

 

Guest May 30, 2020
edited by Guest  May 30, 2020

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