Can someone instruct me to find the area of the shaded triangle ?

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Laia

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I try to solve it but I don't know where to start. Please explain to find the area of the triangle.
 
Laia said:
View attachment 37119
I try to solve it but I don't know where to start. Please explain to find the area of the triangle.
Click to expand...
If you've tried anything at all, please show it to us, because we may be able to show how to use it. There isn't just one way, and the best way for you to use is the one you see for yourself.

Also, please ask any specific questions you have about the problem -- for instance, did you wonder why we aren't told anything about the vertical positioning of the rightmost point of the shaded triangle? Wondering that can help you get a clue to the problem!

But I started by finding the legs of the right triangle at the lower left. Let us know if you see any way to approach that, so we can help you do so.
 
Dr.Peterson said:
If you've tried anything at all, please show it to us, because we may be able to show how to use it. There isn't just one way, and the best way for you to use is the one you see for yourself.

Also, please ask any specific questions you have about the problem -- for instance, did you wonder why we aren't told anything about the vertical positioning of the rightmost point of the shaded triangle? Wondering that can help you get a clue to the problem!

But I started by finding the legs of the right triangle at the lower left. Let us know if you see any way to approach that, so we can help you do so.
Click to expand...
I can only find this part and don't know how to find other sides to find the require area
 

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Laia said:
I can only find this part and don't know how to find other sides to find the require area
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Thanks. That's a good diagram, which is the start of any solution.

You don't really need to find the hypotenuses (just their ratio), but you've used the same similar triangles I had in mind. Great!

Now you can use my subtler hint. Looking at the shaded triangle, the fact that they don't tell you where H is on line BD might remind you that you don't need that information because the area of a triangle depends only on the base and altitude; moving the apex along a line parallel to the base doesn't change the area. If you take the base as FE, which you know, what is the altitude? Then you can find the area!
 
I'm sorry but I don't get it. Would you mind pointing out that on diagram. And I think I can't use the normal way of finding the area of triangle since there's no proof that the required triangle is a right triangle. so I think I need to use the 1/2× a×b× sinQ. But I can't find the proper way to find the necessary sides and angle.
 
Laia said:
I'm sorry but I don't get it. Would you mind pointing out that on diagram. And I think I can't use the normal way of finding the area of triangle since there's no proof that the required triangle is a right triangle. so I think I need to use the 1/2× a×b× sinQ. But I can't find the proper way to find the necessary sides and angle.
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You know that the area of a triangle is 1/2 bh, right?

If you turn your picture on its side so that FE is the base, what is h?

1707760398321.png
 
Dr.Peterson said:
You know that the area of a triangle is 1/2 bh, right?

If you turn your picture on its side so that FE is the base, what is h?

View attachment 37122
Click to expand...
Oh I finally got the point what I've been missing. I didn't realise the way to find the actual height of the triangle and now I just remember it. Thank you sir. This means a lot to me💗
 
Yes, and sorry for the bad written ones cuz I just drew it without pen 🥹
 
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