perplexus.info :: Shapes : Three Squares make a Triangle

Three Squares make a Triangle (Posted on 2019-12-23)

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

Rating: 3.0000 (1 votes)

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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%.

Here's the picture.

Edited on December 23, 2019, 1:34 pm

Posted by Charlie on 2019-12-23 13:32:32

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