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.

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

## 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

## 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.