All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes
Three Squares make a Triangle (Posted on 2019-12-23) Difficulty: 3 of 5
Take three unit squares made of paper.
Select one of the diagonals of each square and rearrange the squares so the three selected diagonals form an equilateral triangle with side length equal to the square root of 2.
The outline of all the paper now forms an irregular hexagon (three angles of which are 90 degrees).
Find the area of this irregular hexagon, and find the percentage of area which is one layer of paper, vs two layers, vs three layers.
What is the shape of the region which is three layers?

No Solution Yet Submitted by Larry    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts partial approximate solution via GSP | Comment 1 of 3
Constructing the figure in Geometer's Sketchpad shows the shape is the same as the outside hexagon. The 90°-angles alternate with 150°-angles. Each side is approximately 0.26795 times that of the outer hexagon so the portion of the outer hexagon that's three layers deep is (0.26795)^2 or .071797 or 7.1797%.

Edited on December 23, 2019, 1:34 pm
  Posted by Charlie on 2019-12-23 13:32:32

Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information