Area of triangle without a tip/top Excuse me if this question is stupid, I am very tired and cannot figure this out
I have a triangle with x-coordinates of the corners of the base as "a" and "b". The height of the triangle is always 1. Therefore the area of the triangle is $\frac{1\cdot(a+b)}{2}$, base times height divided by two. Imagine that the top of the triangle was chopped of by a number between 0 and 1. If it would be chopped of with 0.6, then the height of the "triangle"/trapezoid is 0.6. How would one find the area of this trapezoid using only a, b and the height 0.6?
 A: [EDIT: THE LATEX IS BELOW. I'M A NEW USER HERE AND STILL FIGURING OUT THIS SITE, PARDON ME FOR ANY INCONVENIENCE]
One solution that comes to my mind is that you subtract the area of the missing part of your original triangle from the original area of your triangle. To determine the size of the missing area you would scale it using similar triangles principle (pardon me if English has some other term for this). So the area for the missing part would be when you solve for A1 $$\frac{0.4}{1}=\frac{A_1}{\frac{ah}{2}}$$ $$—> A_1=0.4\cdot\frac{\left(\left|b-a\right|\cdot1\right)}{2}=0.2\cdot\left|b-a\right|$$ Then subtract this result from your original area to solve for this trapezoid: $$A_2=\frac{ah}{2}-A_1=\frac{\left(\left|b-a\right|\cdot1\right)}{2}-0.2\cdot\left|b-a\right|=\left(0.5-0.2\right)\cdot\left|b-a\right|=0.3\left|b-a\right|$$ Hope this is helpful!
A: Well as we know the area of a triangle is $\frac{base\times height}{2}$ so we, in this question have the base $|b-a|$ is the distance between a and b and of course our height $1$. We observe that the smaller triangle we will cut off is similar to our larger triangle so the ratios between the sides will all be the same.
With this suppose our smaller triangle has height $x$, then its base will be $x \times |b-a|$. Putting this together we have the area for our large triangle to be $\frac{|b-a|}{2}$ and the area for our small triangle to be $\frac{|b-a| \times x^2}{2}$. Subtracting the larger from the smaller gives the area of our trapezium.
