What fraction of the 2 x 3 grid of squares is shaded?

C

cruxcriticorum

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If possible, I need to know the process for solving this, not just the answer. Thanks for any help!

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There are two lines that intersect inside the "outer" rectangle. Then you'll know vertices of all the triangles and can calculate areas of those.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
Subhotosh Khan said:
There are two lines that intersect inside the "outer" rectangle. Then you'll know vertices of all the triangles and can calculate areas of those. Please show us what you have tried and exactly where you are stuck. Please follow the rules of posting in this forum, as enunciated at: Please share your work/thoughts about this problem.
Click to expand...
Subhotosh Khan said:
There are two lines that intersect inside the "outer" rectangle. Then you'll know vertices of all the triangles and can calculate areas of those.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
Click to expand...
1604936174576.png

Thanks for your reply. This is what I have so far, just using 1/2b+h, but it doesn't really help that I can see. I need ABE and CDE. Is this the right approach? Or do I need to think differently?
 
You were asked twice to find point E. Now please find it.
 
I might attack this a different way because I see lots of similar triangles.

Label the horizontal line segment ending at B, h-1, the horizontal line segment starting at A, h-3, and the intervening line segment h-2. Similarly, label the vertical line segment descending to A,v-1, proceeding left to right until you label the vertical descending from B as v-4. Now label the little squares, starting at the top left with Sq-1 and proceeding clockwise until you reach the square containing A as Sq-6.

Label as point P the intersection of h-1 and v-3, point Q the intersection of line segment AB and v-3, point R the intersection of line segment h-2 and v-3, point S the intersection of line segmentNote that point D is the intersection of h-3 and v-3. Is it not obvious that triangles AQD and ABF are similar as are triangles ARD and ACF? Can you now compute the area of that portion of the shaded area that lies in squares 2, 5, and 6? How about the portion in square 3?
 
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