# Trapezoid Altitude

• Apr 30th 2012, 04:58 AM
lei
Trapezoid Altitude
Is there a formula to calculate the altitude of a part of a trapezoid?

I would like to solve for X

Thanks,
• Apr 30th 2012, 05:20 AM
Plato
Re: Trapezoid Altitude
Quote:

Originally Posted by lei
Is there a formula to calculate the altitude of a part of a trapezoid?
I would like to solve for X

This can be done. But it is messy.
Let r be the longer base of the red trapezoid.
The using area of the red trapezoid, you can get r in terms of x
Then use the area of the blue trapezoid to solve for x.
• Apr 30th 2012, 05:20 AM
princeps
Re: Trapezoid Altitude
• Apr 30th 2012, 01:46 PM
earboth
Re: Trapezoid Altitude
Quote:

Originally Posted by lei
Is there a formula to calculate the altitude of a part of a trapezoid?

I would like to solve for X

Thanks,

1. Use a coordinate system. Then the smaller parallel of the blue trapezoid is calculated by:

$p = 10-\frac12 x$

2. The area of the blue trapezoid is calculated cosequently:

$A = \frac{10+10-\frac12x}2 \cdot x = 23~\implies~10x-\frac14 x^2 = 23$

3. This is a quadratic where x must be between zero and 10. Solve for x.

4. I've got $x=20-\sqrt{308}$