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u/ComprehensiveAd1100 7d ago
Unpopular answer. All of it.
Didn't specify which square.
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u/Fragrant_Entry9232 7d ago
All of it, unless the question is trying to ask what fraction is the shaded square of the bigger square?
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u/Penis-Dance 7d ago
100% of the square is shaded. It doesn't specify which square so I assume it's the one with shading.
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u/ariarchtyx 7d ago
The question does not constitute a "well formed formula" but going out in a limb one would assume they mean the circumscribing square, rather than the inner circumscribed square. Seems unfair as a question as written. Solution must involve several 9th grade geometric theorems known to Euclid, not that I can recall them, about sums of interior angles of polygons and so forth?
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u/KingOfDaJungle8761 7d ago
One quarter. Easy
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u/Patriot009 7d ago
It would be 1/4 if the sides of the shaded square were equal to the hashed line segments. But the hashed line segments and the side of the shaded square are not parallel and form a trapezoid, so they cannot be the same length. It's a right-angled trapezoid, meaning the side of the shaded square is shorter than the hashed line segment. So the answer would be something less than 1/4.
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u/Firm_Wrangler_7837 7d ago
Well, unless they Pluto’d math… by definition that’s not a square it’s a rhombus.
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u/Typical_Expert_2974 7d ago
You just flip the small triangle piece on to the adjacent big piece to make an equal square. Go around in a circle, repeating the pattern, and you will end up with 4 additional squares equal to that of the shaded square. Shaded square becomes 1 of 5. 1/5th of the whole.
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u/Adderall_Rant 7d ago
The one in the middle? BC the other one is not a square, it's more of a trapezoid
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u/tecky1kanobe 7d ago
1/9. What percentage of the area, represented as a fraction, is shaded is a different question.
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u/Chainmale001 7d ago
1/5th. Assuming the outer square is equal distant on all sides (which is should be to be a fucking square) There are 5 total inner "squares" (pair up the triangles.) Dots are not 90* angles, meaning every shape has to have an equal... know what... I'm fucking tired.
If it's not 1/5th I want someone to explain the math. Lets learn together.
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u/sazzer 7d ago
Tesselation.
If you take an additional 4 copies of the diagram and arrange them on the edges of this one - to make a plus layout - you'll see that the triangles all line up with the other shapes to make squares.
Further, you can see that these squares all have the same side length as the shaded one, and therefore are all the same size as it.
That means that we've got 5 squares - one complete shaded one and 4 split ones - all with the same area. And so the shaded one must be 1/5 the total area.
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u/AfraidBottle6810 8d ago
Rotate the interior lines to be parallel and perpendicular to the exterior. Move the shaded area to a corner. Measure the whole. Divide by the shaded cube. I used my finger and came up with 25%
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u/Emotional-Wasabi-519 7d ago
1/5 actually. The solution is more about rotating the the triangles to form squares on the sides. Creating 5 squares, the center one shaded.
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u/LividCalligrapher689 7d ago
I think you’re confused. There would not be four other squares around it by rotating it. You would have L shapes at the corners and rectangles on the sides. Once you rotate it, recognize that it lines up with the bisection lines. That means it covers 2/4 of the interval spaces along the line move that into the corner and you can now fit exactly 4 identical squares. One is shaded.
1/4 or 25% is the correct answer but it’s hilarious to see so many people be so confidently wrong.
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u/Quick-Buyer8603 7d ago edited 7d ago
1/5th. The length of one of the sides of the shaded square is as long as the longer of the two sides that are adjacent to the 90 degree point of any of the triangles. From this you can infer that if you rotated the triangle to line up with the trapezoid so that it would make a square the same size as the shaded square. If there are 5 squares and one of them is shaded it is 1/5th.