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WebGraphing.com Forum » List all forums » Forum: Calculus Homework Help » Thread: Prove the area of triangle |
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Total posts in this thread: 5 |
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Fabriziolopes
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I have to place a triangle in a coordenate plane and use definite integration to prove that the area is 1/2 base * height. But I'll have to do it in a way that will prove that it will work for all the triangles, I have used right triangle before, but my teacher said to do it in a different way. ---------------------------------------- Cheese |
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pskinner
Joined: Apr 2, 2005 Posts: 797 Status: Offline |
I suggest you place the base along the x-axis and the top vertex on the y-axis. Let the vertex on the y-axis be described: (0,h), so h would then be the height of the triangle. If the base is b, then placing one point on the left hand side at (-a,0), where a>0, would then mean that the point (b-a,0) would be on the x-axis on the right side. Now, you need to get the equations of the line thru (-a,0) and (0,h) and integrate from x=-a to x=0. Then you need to get the equation of the line thru (0,h) and (b-a,h) and integrate from x=0 thru x=b-a. The sum of the integrals should be (1/2)*b*h, if all goes well. Clearly, a needs to drop out somewhere along the way. ---------------------------------------- Principal Skinner |
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Fabriziolopes
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I integrated from -a to 0 h/-a*x+h that was the equation of the line in the left and added the integration from 0 to b-a of h/b-a *x+h the equation of the line in the right and I get 3/2 b*h, but the area of a triangle is just 1/2 b*h. Did I wrote the equation of one of the lines wrong??? ---------------------------------------- Cheese |
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pskinner
Joined: Apr 2, 2005 Posts: 797 Status: Offline |
For the equation of the line on the left, I get (h/a)x+h, so my equation does not have the minus sign. Further, the slope is positive since the line is rising as you read from left to right. For the equation of the line on the right, I get -(h/(b-a))*x+h. The negative slope is consistent with the line falling as you read the graph from left to right. ---------------------------------------- Principal Skinner |
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Fabriziolopes
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I solved it and I got b*h/2 . thanks ---------------------------------------- Cheese |
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Re: Prove the area of triangle