How to calculate dimensions of trapezoid ?

[MSUENG]

I have a problem where I need to calculate the dimensions of a right trapezoid and only have the area, length of the long side and the angle.
The image is attached. Thanks in advance for the help.

 

[Pancho]

Re: Geometry! : Algebra!

You know:

A = total area
t = tangent of known angle
c = known long height

Divide the trap into a rectangle and a right-triangle by drawing a horizontal line at the intersection of the sloped line and the short height. Call:

b = base of rectangle (and triangle)
a = height of triangle
h = height of rectangle (short height of trap)

Then:

(1) A = b ( h + a/2 )
(2) t = b/a
(3) c = a + h

Three equations and three unknowns. Solving (2) for b and (3) for h, and plugging into (1) you get:

A = a?t ( c - a/2 )

that's a quadratic on a:

a^2 - 2ca + 2A/t = 0

a = 0.3095 (the other solution is impossible)
b = 0.5822
h = 0.5363

so A = (0.5822)(0.3095/2 + 0.5363) = 0.4024. √

 

[PaulJSmith]

I don't think you have enough information to calculate that. As I recall, you need three dimensions to calculate the area of a trapezoid. So, given that you already have the area, you would still need another dimension of the other base, the leg, or the height. Not sure the angle will help without one more known length.

 

[MSUENG]

Great! It's been too long since I've had to do that. Thanks for the refresher!