Area of a shape: find area of gray triangle inside square

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LiseyDot05

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Hi everyone. I'm new to this forum but I'm hoping this will be my saviour when I'm sat scratching my head.
My wee son is stuck on this math problem. The square measures 5cm by 5cm. He has the area worked out to be 25cm (he realises it should say 25cm². It is the other 2 questions that he is stuck on & ashamedly, I'm not sure how to explain it to him.
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LiseyDot05 said:
Hi everyone. I'm new to this forum but I'm hoping this will be my saviour when I'm sat scratching my head.
My wee son is stuck on this math problem. The square measures 5cm by 5cm. He has the area worked out to be 25cm (he realises it should say 25cm². It is the other 2 questions that he is stuck on & ashamedly, I'm not sure how to explain it to him.
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It's not clear if the "grey" part only refers to the bottom triangle only or both because the top one looks black to me. Possibly a printing error.
Anyhow, there are different ways to solve it. Without knowing what materials he covered, it's difficult to give you a suggestion. Tell us what you think.
 
If the point where the 4 triangles meet is dead center, then all 4 triangles have the same area.
Can we see the whole problem? There must be more for you to know the dimensions of the square.
 
So for No.11 he thinks it's 25cm²
No.12 - 6.25cm² because its a quarter of the area
No.13 - 12.5cm² because its half of the area.
 
Sorry, but I do not necessarily agree with this. Where did 25 come from? Why are dividing 25 by 4 and 2.
If you really want us to confirm this we need to see the entire problem.
 
@BigBeachBanana
I don't agree with the 25 coming from post #1. This is what the poster claimed the dimensions or area to be. The written problem itself does not state this. That is why I wanted to see the entire problem as there is clearly writing under the picture.
 
That is the entire problem. The writing underneath is separate questions, hence my zooming in on all of that particular question only.
The child measured the square and it is 5cm by 5cm.
 
LiseyDot05 said:
That is the entire problem. The writing underneath is separate questions, hence my zooming in on all of that particular question only.
The child measured the square and it is 5cm by 5cm.
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It would have been helpful if you had initially explained where the 5cm by 5cm came from. Thanks for the update!
Did your son verify that the point where all the triangles meet is the center of the square?
 
Steven G said:
If the point where the 4 triangles meet is dead center, then all 4 triangles have the same area.
Can we see the whole problem? There must be more for you to know the dimensions of the square.
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the lines definitely meet in the center, because the diagonals join the corners of the square
 
Al-Layth said:
the lines definitely meet in the center, because the diagonals join the corners of the square
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I suspect that the author of the problem meant it to be that way, but are you 100% sure that what you are calling diagonals are really straight lines?
For the grade that this problem came from you are correct, but in mathematics one should not assume anything unless it is given or can be proven to be true. That is the number one thing I learned as a student of math.
 
Steven G said:
It would have been helpful if you had initially explained where the 5cm by 5cm came from. Thanks for the update!
Did your son verify that the point where all the triangles meet is the center of the square?
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Sorry, I thought I had when I explained that it measured 5cm by 5cm.
 
Steven G said:
I suspect that the author of the problem meant it to be that way, but are you 100% sure that what you are calling diagonals are really straight lines?
For the grade that this problem came from you are correct, but in mathematics one should not assume anything unless it is given or can be proven to be true. That is the number one thing I learned as a student of math.
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On the other hand, in real-life math, we measure lengths, check straight lines by eye or with a ruler, know from experience that diagonals of a parallelogram (such as a square) bisect one another, and proceed with the appropriate calculation. Not all of life has to be lived as a pure mathematician, and not all of school has to be taught that way.

And if someone tells me, "The square measures 5cm by 5cm", I trust them and help them with the next step, rather than questioning everything.
 
Steven G said:
I suspect that the author of the problem meant it to be that way, but are you 100% sure that what you are calling diagonals are really straight lines?
For the grade that this problem came from you are correct, but in mathematics one should not assume anything unless it is given or can be proven to be true. That is the number one thing I learned as a student of math.
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If we need to explicitly define every assumption of every written assignment - each of those problem-statement will become a "short story"..... may be novella going on for pages.

In my opinion, state your assumptions (if not "given" already) and solve it.
 
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