Find the area of the trapezoidal cross-section of the irrigation canal shown below. Your answer will be in terms of h, w, and θ.
http://www.webassign.net/hgmcalc5/1-5-049.jpg

Question

Find the area of the trapezoidal cross-section of the irrigation canal shown below. Your answer will be in terms of h, w, and θ. 
http://www.webassign.net/hgmcalc5/1-5-049.jpg

noelgreco · Answer

|dw:1346472458903:dw|

Can you calculate p from some trig function of theta ("th" is theta in drawing)

anonymous · Answer

1/2*p*h=area?

noelgreco · Answer

Yeah, but we really need to use p temporarily.

First of all do you see how I got the theta near the p?

anonymous · Answer

its a complmentary angle? sorry im totally lost

noelgreco · Answer

No, actually, it's congruent to the theta given in the problem because alternate interior angles of transversals and parallel lines are congruent.  Does that ring any bells?

anonymous · Answer

kindof but i dont know why you would do that

noelgreco · Answer

Well, if I knew an expression for p, I could say that the long base of the trapezoid was w + 2p, the other base is w, and we have h.  That's all you need for the area of a trapezoid.

noelgreco · Answer

Isn't $$\tan \theta = \frac{ h }{ p}$$

anonymous · Answer

yeah so what would the area be?

anonymous · Answer

tan(theta)*p/h

anonymous · Answer

@NoelGreco