Is there a formula to calculate the altitude of a part of a trapezoid?

Please see the attachment.

I would like to solve for X

Thanks,

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- Apr 30th 2012, 03:58 AMleiTrapezoid Altitude
Is there a formula to calculate the altitude of a part of a trapezoid?

Please see the attachment.

I would like to solve for X

Thanks, - Apr 30th 2012, 04:20 AMPlatoRe: Trapezoid Altitude
- Apr 30th 2012, 04:20 AMprincepsRe: Trapezoid Altitude
- Apr 30th 2012, 12:46 PMearbothRe: Trapezoid Altitude
1. Use a coordinate system. Then the smaller parallel of the blue trapezoid is calculated by:

$\displaystyle p = 10-\frac12 x$

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

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

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

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