Find the area of an equiangular octagon with side lengths 1, 2, 2, 4, 1, 2, 2, 4, in that order.

Guest Aug 5, 2017

#1**+1 **

Best Answer

"*Find the area of an equiangular octagon with side lengths 1, 2, 2, 4, 1, 2, 2, 4, in that order.*"

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Alan
Aug 5, 2017

#2**0 **

Wow....that was nice, Alan.....I couldn't think as to how this might be done....!!!

Could you describe the process you went through to generate this monstrosity ???

CPhill
Aug 5, 2017

#3**+1 **

1. An equiangular octagon must have 8 equal exterior angles that sum to 360°; i.e. they must each be 45°

2. Starting from (0, 0) move a distance 1 (the first length in the list) to the right.

3. Turn 45° anticlockwise and move a distance 2 (the 2nd distance in the list) in that direction. This will take you a further distance 2cos(45°) [or 2/sqrt(2)] in the x-direction, and a distance 2 sin(45°) [also 2/sqrt(2)] in the y-direction.

4. Turn another 45° and move the next distance specified in the list.

5. Keep repeating the above until you land back at (0, 0).

The max and min values of x and y can be found by keeping track of the cumulative sum of stepsize*cos(step*45°) for x, and stepsize*sin(step*45°) for y.

Alan
Aug 5, 2017