Trapezoid inside a triangle

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Loki123

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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.

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Trying to read this carefully, but feeling confused:
the values of all three sides (a, b, c, d).
Click to expand...
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.
 
Last edited:
blamocur said:
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.
Click to expand...
Hahahaha, yeah i messed up, you don't know d. That is the height of the trapezoid too, how do I get that?
 
Loki123 said:
Hahahaha, yeah i messed up, you don't know d. That is the height of the trapezoid too, how do I get that?
Click to expand...
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 [imath]f,d,e[/imath] through [imath]a,b,c[/imath]?
 
blamocur said:
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 [imath]f,d,e[/imath] through [imath]a,b,c[/imath]?
Click to expand...
I think so
 
Can we assume that [imath]a,~b,~\&~c[/imath] are the lengths of the sides of the triangle?
Then [imath]a,~e,~d,~\&~f[/imath] 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 [imath]a[/imath]
is divided by [imath]d[/imath] unto two similar parts (the whole & the smaller part).
The area of the trapezoid is half the sum of [imath]a~\&~d[/imath] times the height of the trapezoid.


[imath][/imath][imath][/imath][imath][/imath]
 
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