Hello All,

Here is a quiz question that relates to figures below. How is it that the triangle below has extra space.

yellow box is moved down and when its adjusted ith green one, this hole comes. Am I concluding it correctly or you are looking for some other response?

Let me explain.

Both the big figures cover 14 squares on X axis and 5 squares on Y axis. The components of the two figures have been moved. The area of the two figures should be same. If the areas are same, how is it that an additional white square can be accomodated in the lower figure? 

Regards,

VK

Hi

 

It's a visual deception, commonly known as an optical illusion (2D). Argument:

A) The way hypotenuse is drawn in both the graphs, irregularly covering the boxes above and below it, is unnatural. This is not a natural, but rather a skewed hypotenuse.

 

Start counting boxes from the X-axis (start from the first coloured box) in figure 1. Go to the 5th box and move to the top most coloured box. Compare the shaded area with its counter part in lower figure (it is higher). Same is with the box 8 topmost area in both the figures.

 

In other words, the points where red and blue triangles' hypotenuse meet are not similar or congruent (explaining A)).

The area covered in lower figure (box 5 + box8) is larger than above figure by 1 box which explains the white box.

I might not be explicit, but that is quite probably the answer.

 

Regards,

Abhishek M

Dear Sir,

 

Since the length and height remains same (red and blue) and over all triangle that means angle remains same in both fig. a and b that means slope is also same in both case when slope and angle is same how can the area covered by red n blue box differ as there surface area is also same in both fig. which is true for yellow n green box also that means surface are will be equal for red n blue n green n yellow in both fig. in such case boxes are placed in the most optimum place to cover the area in fig a and non optimum in fig b.

 

Regards,

Neha Verma

Dear sir ,

Individual block are not same in shape in size cause one hole creation

as below

 

 

The Hypotenuse in the bottom figure is not straight,it's convex, not able to see by the normal eye(@D Illusion), That has resulted in an extra box

Sripathy

The total area covered by all four shapes is same in both the figures (13 x 5 / 2 = 42.5 sq units). The areas of the sub-triangles, red and dark green remain the same,

3x8/2 = 12 and 5x2/2=5, respectively. Hence the difference comes from the rest of the two shapes.

 

Area of the rectangle covered by orange and light green shapes in top figure = 5 x 3 = 15 sq units

Area of the rectangle covered by orange and light green shapes in the bottom figure = 8 x 2 = 16 sq units

Hence the figure at the bottom has 1 sq unit extra, which explains the gap.

Thank you Vishwadeep, for posting this interesting puzzle. Hope you will post more such..

This is an optical illusion... the 2 triangles under discussion (Red and Yellow) are not similar... 

 

Let us see how they are non-similar:

• red triangle:  width 8, height 3
• yellow triangle: width 5, height 2

for these 2 to be similar, their lengths should be proportional.

8/5   is not equal to  3/2...

 

Hence we see this optical illusion and we end up looking for a missing tile.

A very interesting and tricky puzzle. As pointed above, the triangles are not similar...

Optical illusion has been created