# 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.

#### skeeter

MHF Helper

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

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

solve the system

#### bjhopper

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

bjh

#### 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

#### skeeter

MHF Helper
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
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

#### Zellator

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

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?

#### jgv115

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