I am really lost on this problem I have been given in my math assignment and I have tried looking at all my notes and asking my teacher, but he doesn't have any more time to help me, so I will need the rest from you guys 🙂
Anyway, I am supposed to calculate the area of a plate of a kids' swing, which looks like this
I have calculated everything else than the area shown here in red:
And I was told the following by my teacher:
Determine the function for the relevant circle peripheral pieces and
determine, by integrating, the area between the graphs for two
functions.
So I have to find the functions for the relevant curves that will give me the remaining area by doing the above. The thing is I don't know how to do it when I only know the points and the curves shown and I don't know if I can find it by using the circle's equation either.
So how do I do this? Like I said, I know all points and curves
Thanks in advance! 🙂
Best Answer
Presuming you have the radius of the circle. I would calculate the area of the minor segment formed by points G and I using $\frac{r^2}{2}[\theta - \sin(\theta)]$ (in radians). Then find the point of intersection between the curve $LG$ and the vertical line intersecting M which we will call $\lambda$, we can then integrate the curve $LG$ between $\lambda$ and $G$ from which we will then remove the area below $MI$ by integrating under our circle between the two points! This can be done by integrating $y=-(r^2-(x-a)^2)^{0.5}-b$ for circle $(x-a)^2+(y-b)^2=r^2$ between $M$ and $I$.
Hopefully I have explained the method well enough, if you need help with the computation just let me know!