## anonymous 4 years ago 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

1. NoelGreco

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

2. anonymous

1/2*p*h=area?

3. NoelGreco

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

4. anonymous

its a complmentary angle? sorry im totally lost

5. NoelGreco

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?

6. anonymous

kindof but i dont know why you would do that

7. NoelGreco

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.

8. NoelGreco

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

9. anonymous

yeah so what would the area be?

10. anonymous

tan(theta)*p/h

11. anonymous

@NoelGreco