# Height of a Scalene Trapezoid Question

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• Jun 11th 2011, 09:17 AM
Aquameatwad
Height of a Scalene Trapezoid Question
If for a trapezoid , it has base1=40, base2=30, side1=12 & side2=16. How can i find the height?

http://i83.photobucket.com/albums/j3...id-for-geo.jpg

I am stumped. Since it is not isosceles i can't figure it out. Any formulas or guidance?
Much appreciated.
• Jun 11th 2011, 09:35 AM
skeeter
http://img27.imageshack.us/img27/7590/trapproblem.jpg
$\displaystyle h = \sqrt{12^2 - (10-x)^2}$

$\displaystyle h = \sqrt{16^2 - x^2}$

solve the system
• Jun 11th 2011, 12:33 PM
bjhopper
Skeeter equations are correct but they don't compute.This is a faulted quad If 16 is changed to 15 it computes.

bjh
• Jun 11th 2011, 12:53 PM
Zellator
If side 2 will be perpendicular to that created side it has to be 16 right? Why would you change it to 15?
Solving the system, h will be equal to (sqrt3591)/5; which then gives h=~12
Is this the answer?
• Jun 11th 2011, 01:15 PM
skeeter
Quote:

Originally Posted by Zellator
If side 2 will be perpendicular to that created side it has to be 16 right? Why would you change it to 15?
Solving the system, h will be equal to (sqrt3591)/5; which then gives h=~12
Is this the answer?

no ... x works out to be 10.6 , which is impossible. the lower left angle of the trapezoid would have to be obtuse if the other leg = 16
• Jun 11th 2011, 02:00 PM
Zellator
Oh, yes, I got 10.6 also. Nice!
But I didn't know it would be impossible. Thanks!
• Jun 11th 2011, 02:47 PM
Aquameatwad
I got h\approx12. i used herons formula to get the area of the triangle. then back substituted the area into A=1/2bh to get h. Was i lucky or is this another way to get the answer?
• Jun 11th 2011, 05:46 PM
jgv115
Quote:

Originally Posted by Aquameatwad
I got h\approx12. i used herons formula to get the area of the triangle. then back substituted the area into A=1/2bh to get h. Was i lucky or is this another way to get the answer?

That should work but it's unnecessary. Just use pythagoras if you have the required side lengths
• Jun 11th 2011, 05:59 PM
Aquameatwad
Thanks everyone. These are the most helpful forums ever!