# Thread: Height of a Scalene Trapezoid Question

1. ## 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?

I am stumped. Since it is not isosceles i can't figure it out. Any formulas or guidance?
Much appreciated.

2. $h = \sqrt{12^2 - (10-x)^2}$

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

solve the system

3. Skeeter equations are correct but they don't compute.This is a faulted quad If 16 is changed to 15 it computes.

bjh

4. 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?

5. 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

6. Oh, yes, I got 10.6 also. Nice!
But I didn't know it would be impossible. Thanks!

7. 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?

8. 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

9. Thanks everyone. These are the most helpful forums ever!