How can this be true?
That is the question.
I give up. And I mean it. My time is better spent doing other things instead of trying to figure out how this is possible. Please, my dear readers, please be gentle with my poor brain. Some of you are asking too much. It's like trying to decide who's more influential, Paul Poiret or Madeleine Vionnet.
Any ideas?
Because the yellow form has 3 squares side and the green form has 2 square side, and in the 1st picture the side with 2 is with 2 and in the 2nd the 3 square side is with 2….
the empty space appeared in the first pic as a semi 3-d representation of the figure. if you add up all the volume it makes one whole square for the second figure.
Mallory Dash is correct, the two figures are not triangles as the “hypotenuse” of the big “triangle” is not a hypotenuse at all as it is not a single straight line, rather two lines with similar gradients of 2/5 and 3/8, thus you cannot figure the area simply by assuming 1/2bh as it is not a triangle! You will have to figure out the areas of each little part and they do equal each other, but since the triangles have been switched around from one “inward curving” triangle to an “outward curving”, you get the little hole.
13 x 5 = 65 dear…
go check ur calculator…
oh and the gradient for the 2 triangles are different, so maybe that has smth to do with it
dude, its just THERE. the yellow and light green areas add up to 15 units for both of the figures. Its just that the pieces don’t fit as well in the second figure. the aim of the thing is to get you confused and from the looks of it, it succeeded. heehee.
can we just print the above illustration and cut it to know why?
I love these mathematical teasers. The gradient (slope ) of the red and green triangles is different in bothe of the two pictures. Its creates the illusion that the images are the same size but they arent
the second figure does not form a triangle since the slope of the teal triangle is not equal to the slope of the red triangle.
i just think it’s the thick black ink borders — there’s enough slop there to make up 1 square. — and after checking the solution online i suppose my answer was getting at how they pulled off the illusion.
partial credit i think. ;-P
euhm, 13 X 5 = 45 ;-)
45/2 = 22.5
It has to do with the slopes! The “big” triangles in the two pics do not have a perfect slope, because the slopes of the red triangle and the green triangle are actually different. I had to ask someone far smarter than me to help me figure it out!
lulu definitely got it with the mathematical solving.
I’m too lazy for that. I gave up after about 30 seconds.
I cheat!!http://www.puzzle.dse.nl/harder/appearing_area_us.html
the horizontal and vertical lines that form the grid are not parallel, so the bottom part of the grid is smaller than the upper part, hence bottom triangle is smaller than upper triangle. try to overlap the two triangles and you’ll see.
Compare the the two triangles, each made up of puzzle pieces. Look at the hypotenuse (the longest side) of each triangle. At first glance, it looks like a straight line, but it is not. The hypotenuse subtly bows inward in the top triangle and bows outwards in the bottom triangle. This is why the bottom triangle has the greater area.
You can prove this by calculating the angles of the red and green triangles. For the larger triangle to have a straight hypotenuse, the red and green triangles would need to be “similar” – i.e. have all the same angles, just proportionally different side lengths.
Remember the tangent function from trigonometry? The tangent of the leftmost angle of the green triangle is 2/5 = 0.4, so the angle is 21.8 degrees. By the same method, the leftmost angle of the red triangle is 20.6 degrees.
So if the hypotenuse of the green triangle is at a larger angle than the red one, when you line them up with the red one on the bottom, the resultant line will bow in, just like what we see in the picture. Reverse the position of the triangles, and the line bows out.
So the explanation is that the two large, composite triangles are not triangles at all, but trapezoids.
i, too did not get this puzzle.enough of the math.
The slopes of the triangles are not the same.
The yellow/orange piece only fits together the way it does in fig. one. In fig. two the way the pieces are placed will naturally leave a gap.
The reason that the blue and red piece pieces fit in figure two is because the sides that touch the other pieces where the sides in fig. one that where on the outside. This means that they could have made those sides as long/short as needed.
Paul Poiret is… US Vogue won’t feature a whole fashion story for him (8-page, if I’m right, with Natalia V.) if he isn’t.
On the first picture, go ahead and drop the blue shape down to the red shape (so it looks exactly like the second picture. You’ll notice that there are three red squares between the blue shape and the green shape. That’s where your gap comes from.
well its like when you mix gucci shoes and a margiela jacket its ok,..but if you wear margiela top with a gucci bag its just not working,..^^
http://img20.imageshack.us/img20/3481/73095083.png
^they do line up.
ur jus fooled with the color scheme. all the shaded portions of the two triangles are of the same size, except for the red one. the red portion in the lower triangle is smaller than the one on top, hence theres a gap.
here’s the answer;
1A. Before looking at either picture, calculate what the area of this picture
would be if it was a PERFECT triangle (i.e. 13 X 5 squares)
Area = 1/2bh = 1/2(13)(5) = 65/2 = 32 1/2
1B. Area of the top picture
Area = 1 + 2 + 3 + 4
= 1/2(5)(2) + 1/2(8)(3) + 7 + 8
= 5 + 12 + 7 + 8 = 32
1C. Area of the lower picture
Area = 1 + 2 + 3 + 4 + 5
= 1/2(5)(2) + 1/2(8)(3) + 7 + 8 + 1
= 5 + 12 + 7 + 8 + 1 = 33
Neither of the two pictures form a perfect triangle,
but both of them look very close to the outline of a perfect triangle!
Because those to pieces that are joined in the top triangle fit into place. Like puzzle pieces but when you seperate the and put the like in the bottom picture the bar that extends is three units long and the place where it’s resting on is only two units long. The gap comes from the lack of that extra unit.
Cut the pieces out of paper and arrenge then that way and you’ll see that it come out like that
the red triangel on top (second image) doesn’t meet the point where the green triangel (first image) was. there is a slight gap. try overlapping them.