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# Struggling to understand this one... watch

1. Hi all,

Reading this one, I can see that there are 3 separate instances where there are 1/4 of the individual triangles shaded, however can anyone explain this to me in layman's terms. I'm continually getting lost in finding the solution, alternatively (& even better), if someone can suggest material in which this might be explained step by step with additional examples that would be great. I just find the example quite vague & difficult to follow.

Attached Images

2. I have modified the image so to make my advice clearer:

The largest shaded area is 1/4 (as it is a quater of the triangle ABC).

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Now in the attached image to this post, the blue triangle is proportional to the red traiangle, the blue triangle is a quater of the area of triangle ABC.

Note the blue triangle is just triangle ABC but shrunk by a quarter and turned upside down.

What is the area of the second largest shaded triangle IN PROPORTION to the blue triangle? A quater of the blue triangle.

Can you carry on from here?
Attached Images

3. Thanks for the reply Simon, that's helpful. Is another way to look at it as follows:

Essentially breaking it up into 4 larger triangles (so blue x4 makes the larger red triangle) - the blue triangle contains 16 of the smallest segments based on the outlining (of which 5 are shaded), we can then see that as the top portion of the triangle has been shaded (which would be 16 of the smaller segments), we could then total the 3 shaded parts (16+4+1 = 21) & 16x4 = 64, giving us 21/64. Would that score points & hopefully I've been clear there in my workings?

Thanks
James
4. That sounds good as well, although some simple explanation of how you obtained each value would be key.

The biggest one is a quarter of the whole triangle = 1/4

The second biggest one is a quarter of a quarter of the triangle = 1/4 x 1/4 = 1/16 (of the whole triangle)

And the smallest one is a quarter of a quarter of a quarter of a triangle = 1/4 x 1/4 x 1/4 = 1/64 ( of the whole triangle)

Adding those all together ( 1/4 + 1/16 + 1/64) you get 21/64 of the whole triangle

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