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# irregular shapes

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

Aug 5, 2017

#1
+27578
+1

"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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Aug 5, 2017

#1
+27578
+1

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

.

Alan Aug 5, 2017
#2
+98197
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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 ???

Aug 5, 2017
edited by CPhill  Aug 5, 2017
#3
+27578
+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
edited by Alan  Aug 5, 2017
#4
+98197
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OK, Thanks!!

Aug 5, 2017