Triangle area in a trapezoid

Luj8n

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Area of trapezoid is 234. I need to find the area of the darker triangle. Can anyone help me?
 

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Dr.Peterson

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Draw a horizontal line through E, and think about the parts above and below that line.

But before we actually do that, we need to clarify something. You drew the figure on graph paper, as if we know all the exact positions and proportions. Is that correct, or do we only know that it is a trapezoid? Do we even know that it is not isosceles, as shown?

Further, I can see many different ways to approach the problem, so I'd like to start with whatever ideas you have, rather than just picking a method that I happen to like, which might use ideas you don't know. For example, we could use formulas for areas of triangles and trapezoids; or we could use a geometrical construction, or we could use some theorems about areas.
 

Luj8n

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Draw a horizontal line through E, and think about the parts above and below that line.

But before we actually do that, we need to clarify something. You drew the figure on graph paper, as if we know all the exact positions and proportions. Is that correct, or do we only know that it is a trapezoid? Do we even know that it is not isosceles, as shown?

Further, I can see many different ways to approach the problem, so I'd like to start with whatever ideas you have, rather than just picking a method that I happen to like, which might use ideas you don't know. For example, we could use formulas for areas of triangles and trapezoids; or we could use a geometrical construction, or we could use some theorems about areas.
Hey! I'm not a native English speaker, so I don't understand what those big words mean xD. But all we know is that we don't know the actual positions and proportions. Btw I'm in 8th class so I don't really know that much but I'm pretty good in Maths. I don't really care with which way we approach this problem. :)
 

Luj8n

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Also, we know that CE = ED.
 

Dr.Peterson

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The issue is, what have you learned that you could use? I don't want to confuse you by suggesting things you don't know!

It may also be helpful to know which words you'd like clarified; you can ask!
 

Luj8n

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You can use any method ;) . Btw I didn't know what isosceles means but i just googled it (it's not).
 

Dr.Peterson

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Shall I use calculus, then??

Honestly, I can't help you without knowing what help you need. Anything at all that you can show me, such as a formula for the area of a trapezoid, will give me a place to start. What topics have you been studying that this is meant to help you learn?
 

Luj8n

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Sooo... I know how to find the area of a trapezoid: S=(a+b):2×h. My math teacher just showed this problem after the class and my friend and I don't know how to solve this.
 

Luj8n

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Annnd I don't really know what calculus is ... This should be solved in a simple way I think.
 

Dr.Peterson

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Well, here's one way to start.

Find the areas of the two unshaded triangles (given a, b, and h). Then subtract the sum from the area of the trapezoid.

It would still be really helpful if I knew what parts of geometry you have learned, so I would know what to expect you to be able to follow. There are several fun ways to see the answer rather quickly, if you knew enough. I'm having to avoid the fun to keep it simple!
 

Luj8n

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We don't learn geometry that much right now. But juat show a way and I will see if I'll understand. :)
 

Dr.Peterson

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I did!

Try it. You're learning something; the way to learn is to try solving the problems you are given. And the way to ask for help is to cooperate with the helper.

It sounds like anything I suggest will probably be beyond you; that makes it all the more important that you show something of what you've learned. My suggestion requires only a little more than using the formulas for area of a trapezoid and of a triangle, and a little bit of algebra.
 

Luj8n

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Actually I'm pretty good with algebra :) . Btw what does it mean "given a, b and h" (I understand what's h and a, b).
 

Dr.Peterson

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Now we're getting somewhere. You've written expressions for the two triangle areas in terms of the unknown a, b, and h (which is what I meant by "given": treating those variables as if we know them).

Now add those expressions together, and subtract from the area of the trapezoid. You should see an interesting fact.
 

Luj8n

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Wow. I see now, I didn't think to do this... I got (a+b):4×h. I know that the triangle's are is (117) 1/2 of the trapezoid's. But how to write that?
 

Dr.Peterson

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I'm not sure what you're asking for. You've found the answer, 234/2 = 117. And you did it by finding that the unshaded area and the shaded area are each half of the trapezoid. What more is there to write?

Now, what you might want to do next is to ponder how else you might have seen such a simple answer. There are many ways I can think of to modify the drawing to make it "obvious" if you look at it the right way, and doing that can improve your ability to see how to solve a problem.
 

Luj8n

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Ok ty ;) . I understand now. It was a pleasure to meet you. :)
 
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