Trapezoid inside a triangle

[Loki123]

Please read this carefully because it explains the problem more than the picture. You have a triangle, you know the values of all three sides (a, b, c, d). A parallel line to the longest line is drawn in the triangle to create a trapezoid. Calculate the area of that trapezoid if you know the sum of all trapezoid side.
*There are numbers involved here but I cannot remember them correctly so all I am asking for is the method to do this. Thank you.

 

[blamocur]

Trying to read this carefully, but feeling confused:

the values of all three sides (a, b, c, d).

Reminds me of an old joke that people can be divided into three groups -- those who can count and those who cannot

More seriously: you have only one degree of freedom here: the relative height of the parallel line. Using that as a variable you would get a relatively simple equation.

 

[Loki123]

Trying to read this carefully, but feeling confused:

Reminds me of an old joke that people can be divided into three groups -- those who can count and those who cannot

More seriously: you can only one degree of freedom here: the relative height of the parallel line. Using that as a variable you would get a relatively simple equation.

Hahahaha, yeah i messed up, you don't know d. That is the height of the trapezoid too, how do I get that?

 

[blamocur]

Hahahaha, yeah i messed up, you don't know d. That is the height of the trapezoid too, how do I get that?

I don't think you need the absolute height, but only the relative one. For example, if you know that your line is at 1/3 of the height can you express $f,d,e$ through $a,b,c$?

 

[Deleted member 4993]

Hahahaha, yeah i messed up, you don't know d. That is the height of the trapezoid too, how do I get that?

You have two similar triangles. Use the proportional sides theorem.

 

[Loki123]

I don't think you need the absolute height, but only the relative one. For example, if you know that your line is at 1/3 of the height can you express $f,d,e$ through $a,b,c$?

I think so

 

[Loki123]

You have two similar triangles. Use the proportional sides theorem.

You mean the big one and the one that has d as the base?

 

[Deleted member 4993]

You mean the big one and the one that has d as the base?

What do you think?

 

[pka]

Can we assume that $a,~b,~\&~c$ are the lengths of the sides of the triangle?
Then $a,~e,~d,~\&~f$ are the lengths of the sides of the trapezoid?
As Mr. Khan has noted there are two similar triangles. An altitude from the apex to the base $a$
is divided by $d$ unto two similar parts (the whole & the smaller part).
The area of the trapezoid is half the sum of $a~\&~d$ times the height of the trapezoid.


$$$$$$

 

[Loki123]

What do you think?

I think yes but I have to check