I have a problem where I am given a square with each side = to 3, that is stretched until points A and B are at a distance of 3 away from each other. Additionally, the length of the sides do not "stretch".
I thought that because area is base * height, that the area would not change due to this transformation.
In this case, the area of the square before transformation is 9, but the area of the rhombus is 7.794.
Why does the area change?
Why is the area of the rhombus still not base times height?
Please note, I understand how to get the area of the rhombus – it just does not make sense intuitively and conflicts with the area of a parallelogram being b times h idea.
Best Answer
It IS base times height but the height has changed.
The height is the perpendicular from line to line. As a square the height was 3 as the sides were perpendicular. You've squished the square over while keeping the sides the same but the sides are no longer perpendicular. So the height is no longer the same thing as the sides. The height is now less than 3.