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    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.

    Thanks in advance!
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    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).

    ------------------------------------------------------------------------------------------------

    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?
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    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
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    That sounds good as well, although some simple explanation of how you obtained each value would be key.
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    Hi , haven't read to see if it has been thoroughly answered already but you can see, for the shaded triangles,:

    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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