Root of four times five, which is equal to two times Square root of 20, which is equal to the square So, this is going to be equal to the square root of four plus 16. Change in y is negative four but we're going to square it, so it's going to become a positive 16. Of our change in x squared plus our change in y squared. So, it's going to be the square root of two squared plus our, let me write that radicalĪ little bit better. "Six minus four is two." You see that visually, here. "Our starting point, our x-value is four. If you want to do that purely numerically, we would say, "Okay, ourĮndpoint, our x value is six. We're going from X equalsįour to x equals six. We're going from W to N, our change in x is two. So, h is going to be equal to, and so, what is our, if Root of nine times five which is equal to three Plus three squared which is going to be equal to, it's going to be equal to 36 plus nine, which is 45, so, square root of 45 which is equal to the square The hypotenuse, here, is going to be the square root of change in x squared, six squared, plus change in y squared, So, just applying the Pythagorean Theorem to find the length of Our change in y, we are going from, we are going from y equals, yĮquals five to y equals eight. Going from x is at negative two, x is going from negative Triangle, if you like, like this, to figure those things out. Well, let's see, if we're going from, we could set up a right Of change in x squared plus change in y squared. So, b two, once again, change in x squared plus the square root Root of 36 times five which is equal to, square root of 36 is 6, so six square roots of five. So, the square root of 144 plus 36 is one hundred, one hundred and 80 which is equal to, let's Squared, so plus six squared, and this is going to beĮqual to 144 plus 36. The Pythagorean Theorem, this is going to be our change in x, squared, 12 squared, plus our change in y, The distance formula is just an application of So, the length of that hypotenuse, from the Pythagorean Theorem, and, as I mentioned, That's just the hypotenuse of this right triangle And, the segment that we care about, its length that we care about, So, we could say our change in y equal to five minus negative one which, of course, is equal to six. And, our change in in y, our change in y, we are going from y equals To eight minus negative four which is equal to 12. And, notice, we're goingįrom x equals negative four to x equals eight, as w go from C to L. Pythagorean Theorem." So, this is going to be the square root of ourĬhange in x squared, so our change in x is going The distance formula is just "an application of the The distance formula," and you could say, "Well, Look, we know what these, "the coordinates of these points are." You could say, "Let's use What is b one going to be? B one is the length of segment CL and you could say, "We'll Anyway, let's see how weĬould figure this out. You an even break out,īreak down a trapezoid into two triangles and a rectangle, which is one way to think about it. We have multiple videos talking about the proofs or how we came up with this formula. And, once again, if this isĬompletely unfamiliar to you or of you're curious, Lengths of each of these, if we know each of these values, which are the lengths of these segments, then we can evaluate the area Notice it intersects the, base one, I guess you could say segmentĬL at a right angle, here. And then, our height, our height h, well, that would just be an altitude and they did one in a dotted line, here. Length of segment OW, or b two would be the length of segment OW, right over there. Base two, base two, that could, we'll do that in a different color. To be our height over here? Well, we could call base one, we could call that segment CL, so it would be the length of And, so what are our bases here? What are, and what is going The lengths of the bases, we could say base one plusīase two times the height. Trapezoid, just put simply, is equal to the average of And, like always, pause this video and see if you can figure it out. T.- So we have a trapezoid here on the coordinate planeĪnd what we want to do is find the area of this trapezoid, R.input2() shapeptr = &r shapeptr->display()
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