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,
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 $\displaystyle x=20-\sqrt{308}$