A square and an equilateral triangle are divided in several polygons. What is the proportion yellow : blue?
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Solution
The proportion yellow : blue is 1 : 1.
![](https://mirangu.com/wp-content/uploads/2022/03/RootCauseSolution.jpg)
Thanks to @RonySarker71 I see the light, at last ☺
In my diagram, deduct area of ADE from that of “purple” and “ABCD” to prove that the remainders are also equal.
Visual solution
![](https://mirangu.com/wp-content/uploads/2022/03/RootCauseDavid.jpg)
Poem
Why the root cause
For a painting remembering Mondrian ?
Specialist of abstract art
A special vocabulary
For figures of geometry
Such highly utopia
Mondrian says art is higher than reality
In order to create universal beauty
And intimate spirituality
To come close to harmony
![](https://mirangu.com/wp-content/uploads/2022/03/RootCauseBella.jpg)
One reply on “The root cause”
Let ABCD ( clockwise with A at top left) and DCE be the square and the equilateral triangle. F and G are the midpoints of AD and BC. AE and BE intersect FG at M and N respectively.
Let AB=2. By symmetry, the triangles ADE and BCE are congruent and also the triangles AFM and BGN.
Rectangle ABGF area is 2*1 = 2….
(1)
triangle ADE and BCE total area is 2*(1/2)*2*1 = 2…..(2)
Equating (1) and (2) and subtracting the sum of areas of the triangles AFM and BGN from both sides,
area of ABNM = sum area of FMED and GNEC.
which is same as,
Blue area = Yellow area.
Hence the ratio is 1:1.